************************************************************************* * * * README * * * ************************************************************************* * This file contains cycle factorization classes description for * * Validity Preserving Transformations group (3359232 transformations * * in total - all possible combinations of bands/stacks permutations, * * rows/columns in the same band/stack permutations and transposing). * * Common 9 x 9 cells sudoku grid is assumed. * * * * Each class description contains number of class (1-163), number of * * transformations beloning to that class, cycle structure description * * (complete factorization into disjoint cycles is assumed), sample * * transformations, presented in 2 views - cycle notation and notation * * showing sample transformation's generation way. * * * * Letters denote basic transformations used (type of permutation): * * * * B - bands permutation * * r - rows of the top band permutation * * s - rows of the middle band permutation * * t - rows of the bottom band permutation * * S - stacks permutation * * c - columns of the left stack permutation * * d - columns of the central stack permutation * * e - columns of the rigth stack permutation * * T - transposing * * * * Digit, folowing each letter denotes kind of permutation. * * For all permutation, except transposing, such * * permutations are assumed: * * * * 0 - {1,2,3} (Do nothing) * * 1 - {1,3,2} (Swapping 2-nd and 3-rd elements) * * 2 - {2,1,3} (Swapping 1-st and 2-nd elements) * * 3 - {3,2,1} (Swapping 1-st and 3-rd elements) * * 4 - {2,3,1} (Left cyclic shift) * * 5 - {3,1,2} (Right cyclic shift) * * * * For transposing such permutations are assumed: * * * * 0 - Do nothing * * 1 - Transpose grid (i.e. exchange rows and columns) * * * * All transformationsare applied from left to right - bands * * trasformation applied first and transposing is * * applied last. * * * * For example, notation B1r0s0t1S0c1d4e4T1 implies such sequence of * * transformations: * * * * 1. Swapping middle and bottom bands * * 2. Swapping rows r8/r9 * * 3. Swapping columns c2/c3 * * 4. Cyclic permutation of columns: c4 -> c6, c5 -> c4, c6 -> c5 * * 5. Cyclic permutation of columns: c7 -> c9, c8 -> c7, c9 -> c8 * * 6. Transposing * * * ************************************************************************* Cycle factorization class 1 contains 1 transformations Cycle length: 1, count: 81 Sample: B0r0s0t0S0c0d0e0T0 (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)(62)(63)(64)(65)(66)(67)(68)(69)(70)(71)(72)(73)(74)(75)(76)(77)(78)(79)(80)(81) Cycle factorization class 2 contains 3429 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 36 Sample: B0r0s0t0S0c0d0e0T1 (1)(10 2)(19 3)(28 4)(37 5)(46 6)(55 7)(64 8)(73 9)(11)(20 12)(29 13)(38 14)(47 15)(56 16)(65 17)(74 18)(21)(30 22)(39 23)(48 24)(57 25)(66 26)(75 27)(31)(40 32)(49 33)(58 34)(67 35)(76 36)(41)(50 42)(59 43)(68 44)(77 45)(51)(60 52)(69 53)(78 54)(61)(70 62)(79 63)(71)(80 72)(81) Cycle factorization class 3 contains 18 transformations Cycle length: 1, count: 63 Cycle length: 2, count: 9 Sample: B0r0s0t0S0c0d0e1T0 (1)(2)(3)(4)(5)(6)(7)(9 8)(10)(11)(12)(13)(14)(15)(16)(18 17)(19)(20)(21)(22)(23)(24)(25)(27 26)(28)(29)(30)(31)(32)(33)(34)(36 35)(37)(38)(39)(40)(41)(42)(43)(45 44)(46)(47)(48)(49)(50)(51)(52)(54 53)(55)(56)(57)(58)(59)(60)(61)(63 62)(64)(65)(66)(67)(68)(69)(70)(72 71)(73)(74)(75)(76)(77)(78)(79)(81 80) Cycle factorization class 4 contains 11664 transformations Cycle length: 1, count: 7 Cycle length: 2, count: 21 Cycle length: 4, count: 8 Sample: B0r0s0t0S0c0d0e1T1 (1)(10 2)(19 3)(28 4)(37 5)(46 6)(55 7)(73 9 64 8)(11)(20 12)(29 13)(38 14)(47 15)(56 16)(74 18 65 17)(21)(30 22)(39 23)(48 24)(57 25)(75 27 66 26)(31)(40 32)(49 33)(58 34)(76 36 67 35)(41)(50 42)(59 43)(77 45 68 44)(51)(60 52)(78 54 69 53)(61)(79 63 70 62)(80 81 72 71) Cycle factorization class 5 contains 12 transformations Cycle length: 1, count: 54 Cycle length: 3, count: 9 Sample: B0r0s0t0S0c0d0e4T0 (1)(2)(3)(4)(5)(6)(8 9 7)(10)(11)(12)(13)(14)(15)(17 18 16)(19)(20)(21)(22)(23)(24)(26 27 25)(28)(29)(30)(31)(32)(33)(35 36 34)(37)(38)(39)(40)(41)(42)(44 45 43)(46)(47)(48)(49)(50)(51)(53 54 52)(55)(56)(57)(58)(59)(60)(62 63 61)(64)(65)(66)(67)(68)(69)(71 72 70)(73)(74)(75)(76)(77)(78)(80 81 79) Cycle factorization class 6 contains 7776 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 15 Cycle length: 3, count: 1 Cycle length: 6, count: 7 Sample: B0r0s0t0S0c0d0e4T1 (1)(10 2)(19 3)(28 4)(37 5)(46 6)(64 8 73 9 55 7)(11)(20 12)(29 13)(38 14)(47 15)(65 17 74 18 56 16)(21)(30 22)(39 23)(48 24)(66 26 75 27 57 25)(31)(40 32)(49 33)(67 35 76 36 58 34)(41)(50 42)(68 44 77 45 59 43)(51)(69 53 78 54 60 52)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 7 contains 54 transformations Cycle length: 1, count: 45 Cycle length: 2, count: 18 Sample: B0r0s0t0S0c0d1e1T0 (1)(2)(3)(4)(6 5)(7)(9 8)(10)(11)(12)(13)(15 14)(16)(18 17)(19)(20)(21)(22)(24 23)(25)(27 26)(28)(29)(30)(31)(33 32)(34)(36 35)(37)(38)(39)(40)(42 41)(43)(45 44)(46)(47)(48)(49)(51 50)(52)(54 53)(55)(56)(57)(58)(60 59)(61)(63 62)(64)(65)(66)(67)(69 68)(70)(72 71)(73)(74)(75)(76)(78 77)(79)(81 80) Cycle factorization class 8 contains 34992 transformations Cycle length: 1, count: 5 Cycle length: 2, count: 10 Cycle length: 4, count: 14 Sample: B0r0s0t0S0c0d1e1T1 (1)(10 2)(19 3)(28 4)(46 6 37 5)(55 7)(73 9 64 8)(11)(20 12)(29 13)(47 15 38 14)(56 16)(74 18 65 17)(21)(30 22)(48 24 39 23)(57 25)(75 27 66 26)(31)(49 33 40 32)(58 34)(76 36 67 35)(50 51 42 41)(59 52 60 43)(77 54 69 44)(68 53 78 45)(61)(79 63 70 62)(80 81 72 71) Cycle factorization class 9 contains 72 transformations Cycle length: 1, count: 36 Cycle length: 2, count: 9 Cycle length: 3, count: 9 Sample: B0r0s0t0S0c0d1e4T0 (1)(2)(3)(4)(6 5)(8 9 7)(10)(11)(12)(13)(15 14)(17 18 16)(19)(20)(21)(22)(24 23)(26 27 25)(28)(29)(30)(31)(33 32)(35 36 34)(37)(38)(39)(40)(42 41)(44 45 43)(46)(47)(48)(49)(51 50)(53 54 52)(55)(56)(57)(58)(60 59)(62 63 61)(64)(65)(66)(67)(69 68)(71 72 70)(73)(74)(75)(76)(78 77)(80 81 79) Cycle factorization class 10 contains 46656 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 6 Cycle length: 3, count: 1 Cycle length: 4, count: 5 Cycle length: 6, count: 5 Cycle length: 12, count: 1 Sample: B0r0s0t0S0c0d1e4T1 (1)(10 2)(19 3)(28 4)(46 6 37 5)(64 8 73 9 55 7)(11)(20 12)(29 13)(47 15 38 14)(65 17 74 18 56 16)(21)(30 22)(48 24 39 23)(66 26 75 27 57 25)(31)(49 33 40 32)(67 35 76 36 58 34)(50 51 42 41)(68 53 78 45 59 52 69 44 77 54 60 43)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 11 contains 24 transformations Cycle length: 1, count: 27 Cycle length: 3, count: 18 Sample: B0r0s0t0S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(28)(29)(30)(32 33 31)(35 36 34)(37)(38)(39)(41 42 40)(44 45 43)(46)(47)(48)(50 51 49)(53 54 52)(55)(56)(57)(59 60 58)(62 63 61)(64)(65)(66)(68 69 67)(71 72 70)(73)(74)(75)(77 78 76)(80 81 79) Cycle factorization class 12 contains 18144 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 3, count: 2 Cycle length: 6, count: 11 Sample: B0r0s0t0S0c0d4e4T1 (1)(10 2)(19 3)(37 5 46 6 28 4)(64 8 73 9 55 7)(11)(20 12)(38 14 47 15 29 13)(65 17 74 18 56 16)(21)(39 23 48 24 30 22)(66 26 75 27 57 25)(40 41 50 51 33 31)(49 42 32)(67 44 77 54 60 34)(76 45 59 52 69 35)(58 43 68 53 78 36)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 13 contains 90 transformations Cycle length: 1, count: 27 Cycle length: 2, count: 27 Sample: B0r0s0t0S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(28)(30 29)(31)(33 32)(34)(36 35)(37)(39 38)(40)(42 41)(43)(45 44)(46)(48 47)(49)(51 50)(52)(54 53)(55)(57 56)(58)(60 59)(61)(63 62)(64)(66 65)(67)(69 68)(70)(72 71)(73)(75 74)(76)(78 77)(79)(81 80) Cycle factorization class 14 contains 58320 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 4, count: 18 Sample: B0r0s0t0S0c1d1e1T1 (1)(19 3 10 2)(28 4)(46 6 37 5)(55 7)(73 9 64 8)(20 21 12 11)(29 22 30 13)(47 24 39 14)(38 23 48 15)(56 25 57 16)(74 27 66 17)(65 26 75 18)(31)(49 33 40 32)(58 34)(76 36 67 35)(50 51 42 41)(59 52 60 43)(77 54 69 44)(68 53 78 45)(61)(79 63 70 62)(80 81 72 71) Cycle factorization class 15 contains 108 transformations Cycle length: 1, count: 18 Cycle length: 2, count: 18 Cycle length: 3, count: 9 Sample: B0r0s0t0S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(28)(30 29)(31)(33 32)(35 36 34)(37)(39 38)(40)(42 41)(44 45 43)(46)(48 47)(49)(51 50)(53 54 52)(55)(57 56)(58)(60 59)(62 63 61)(64)(66 65)(67)(69 68)(71 72 70)(73)(75 74)(76)(78 77)(80 81 79) Cycle factorization class 16 contains 69984 transformations Cycle length: 1, count: 2 Cycle length: 2, count: 1 Cycle length: 3, count: 1 Cycle length: 4, count: 8 Cycle length: 6, count: 3 Cycle length: 12, count: 2 Sample: B0r0s0t0S0c1d1e4T1 (1)(19 3 10 2)(28 4)(46 6 37 5)(64 8 73 9 55 7)(20 21 12 11)(29 22 30 13)(47 24 39 14)(38 23 48 15)(65 26 75 18 56 25 66 17 74 27 57 16)(31)(49 33 40 32)(67 35 76 36 58 34)(50 51 42 41)(68 53 78 45 59 52 69 44 77 54 60 43)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 17 contains 72 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 9 Cycle length: 3, count: 18 Sample: B0r0s0t0S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(28)(30 29)(32 33 31)(35 36 34)(37)(39 38)(41 42 40)(44 45 43)(46)(48 47)(50 51 49)(53 54 52)(55)(57 56)(59 60 58)(62 63 61)(64)(66 65)(68 69 67)(71 72 70)(73)(75 74)(77 78 76)(80 81 79) Cycle factorization class 18 contains 46656 transformations Cycle length: 1, count: 1 Cycle length: 3, count: 2 Cycle length: 4, count: 2 Cycle length: 6, count: 7 Cycle length: 12, count: 2 Sample: B0r0s0t0S0c1d4e4T1 (1)(19 3 10 2)(37 5 46 6 28 4)(64 8 73 9 55 7)(20 21 12 11)(38 23 48 15 29 22 39 14 47 24 30 13)(65 26 75 18 56 25 66 17 74 27 57 16)(40 41 50 51 33 31)(49 42 32)(67 44 77 54 60 34)(76 45 59 52 69 35)(58 43 68 53 78 36)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 19 contains 9440 transformations Cycle length: 3, count: 27 Sample: B0r0s0t0S0c4d4e4T0 (2 3 1)(5 6 4)(8 9 7)(11 12 10)(14 15 13)(17 18 16)(20 21 19)(23 24 22)(26 27 25)(29 30 28)(32 33 31)(35 36 34)(38 39 37)(41 42 40)(44 45 43)(47 48 46)(50 51 49)(53 54 52)(56 57 55)(59 60 58)(62 63 61)(65 66 64)(68 69 67)(71 72 70)(74 75 73)(77 78 76)(80 81 79) Cycle factorization class 20 contains 279936 transformations Cycle length: 3, count: 3 Cycle length: 6, count: 12 Sample: B0r0s0t0S0c4d4e4T1 (10 11 20 21 3 1)(19 12 2)(37 14 47 24 30 4)(46 15 29 22 39 5)(28 13 38 23 48 6)(64 17 74 27 57 7)(73 18 56 25 66 8)(55 16 65 26 75 9)(40 41 50 51 33 31)(49 42 32)(67 44 77 54 60 34)(76 45 59 52 69 35)(58 43 68 53 78 36)(70 71 80 81 63 61)(79 72 62) Cycle factorization class 21 contains 81 transformations Cycle length: 1, count: 49 Cycle length: 2, count: 16 Sample: B0r0s0t1S0c0d0e1T0 (1)(2)(3)(4)(5)(6)(7)(9 8)(10)(11)(12)(13)(14)(15)(16)(18 17)(19)(20)(21)(22)(23)(24)(25)(27 26)(28)(29)(30)(31)(32)(33)(34)(36 35)(37)(38)(39)(40)(41)(42)(43)(45 44)(46)(47)(48)(49)(50)(51)(52)(54 53)(55)(56)(57)(58)(59)(60)(61)(63 62)(73 64)(74 65)(75 66)(76 67)(77 68)(78 69)(79 70)(81 71)(80 72) Cycle factorization class 22 contains 108 transformations Cycle length: 1, count: 42 Cycle length: 2, count: 6 Cycle length: 3, count: 7 Cycle length: 6, count: 1 Sample: B0r0s0t1S0c0d0e4T0 (1)(2)(3)(4)(5)(6)(8 9 7)(10)(11)(12)(13)(14)(15)(17 18 16)(19)(20)(21)(22)(23)(24)(26 27 25)(28)(29)(30)(31)(32)(33)(35 36 34)(37)(38)(39)(40)(41)(42)(44 45 43)(46)(47)(48)(49)(50)(51)(53 54 52)(55)(56)(57)(58)(59)(60)(62 63 61)(73 64)(74 65)(75 66)(76 67)(77 68)(78 69)(80 72 79 71 81 70) Cycle factorization class 23 contains 486 transformations Cycle length: 1, count: 35 Cycle length: 2, count: 23 Sample: B0r0s0t1S0c0d1e1T0 (1)(2)(3)(4)(6 5)(7)(9 8)(10)(11)(12)(13)(15 14)(16)(18 17)(19)(20)(21)(22)(24 23)(25)(27 26)(28)(29)(30)(31)(33 32)(34)(36 35)(37)(38)(39)(40)(42 41)(43)(45 44)(46)(47)(48)(49)(51 50)(52)(54 53)(55)(56)(57)(58)(60 59)(61)(63 62)(73 64)(74 65)(75 66)(76 67)(78 68)(77 69)(79 70)(81 71)(80 72) Cycle factorization class 24 contains 648 transformations Cycle length: 1, count: 28 Cycle length: 2, count: 13 Cycle length: 3, count: 7 Cycle length: 6, count: 1 Sample: B0r0s0t1S0c0d1e4T0 (1)(2)(3)(4)(6 5)(8 9 7)(10)(11)(12)(13)(15 14)(17 18 16)(19)(20)(21)(22)(24 23)(26 27 25)(28)(29)(30)(31)(33 32)(35 36 34)(37)(38)(39)(40)(42 41)(44 45 43)(46)(47)(48)(49)(51 50)(53 54 52)(55)(56)(57)(58)(60 59)(62 63 61)(73 64)(74 65)(75 66)(76 67)(78 68)(77 69)(80 72 79 71 81 70) Cycle factorization class 25 contains 216 transformations Cycle length: 1, count: 21 Cycle length: 2, count: 3 Cycle length: 3, count: 14 Cycle length: 6, count: 2 Sample: B0r0s0t1S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(28)(29)(30)(32 33 31)(35 36 34)(37)(38)(39)(41 42 40)(44 45 43)(46)(47)(48)(50 51 49)(53 54 52)(55)(56)(57)(59 60 58)(62 63 61)(73 64)(74 65)(75 66)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 26 contains 810 transformations Cycle length: 1, count: 21 Cycle length: 2, count: 30 Sample: B0r0s0t1S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(28)(30 29)(31)(33 32)(34)(36 35)(37)(39 38)(40)(42 41)(43)(45 44)(46)(48 47)(49)(51 50)(52)(54 53)(55)(57 56)(58)(60 59)(61)(63 62)(73 64)(75 65)(74 66)(76 67)(78 68)(77 69)(79 70)(81 71)(80 72) Cycle factorization class 27 contains 972 transformations Cycle length: 1, count: 14 Cycle length: 2, count: 20 Cycle length: 3, count: 7 Cycle length: 6, count: 1 Sample: B0r0s0t1S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(28)(30 29)(31)(33 32)(35 36 34)(37)(39 38)(40)(42 41)(44 45 43)(46)(48 47)(49)(51 50)(53 54 52)(55)(57 56)(58)(60 59)(62 63 61)(73 64)(75 65)(74 66)(76 67)(78 68)(77 69)(80 72 79 71 81 70) Cycle factorization class 28 contains 648 transformations Cycle length: 1, count: 7 Cycle length: 2, count: 10 Cycle length: 3, count: 14 Cycle length: 6, count: 2 Sample: B0r0s0t1S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(28)(30 29)(32 33 31)(35 36 34)(37)(39 38)(41 42 40)(44 45 43)(46)(48 47)(50 51 49)(53 54 52)(55)(57 56)(59 60 58)(62 63 61)(73 64)(75 65)(74 66)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 29 contains 12960 transformations Cycle length: 3, count: 21 Cycle length: 6, count: 3 Sample: B0r0s0t1S0c4d4e4T0 (2 3 1)(5 6 4)(8 9 7)(11 12 10)(14 15 13)(17 18 16)(20 21 19)(23 24 22)(26 27 25)(29 30 28)(32 33 31)(35 36 34)(38 39 37)(41 42 40)(44 45 43)(47 48 46)(50 51 49)(53 54 52)(56 57 55)(59 60 58)(62 63 61)(74 66 73 65 75 64)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 30 contains 36 transformations Cycle length: 1, count: 36 Cycle length: 3, count: 15 Sample: B0r0s0t4S0c0d0e4T0 (1)(2)(3)(4)(5)(6)(8 9 7)(10)(11)(12)(13)(14)(15)(17 18 16)(19)(20)(21)(22)(23)(24)(26 27 25)(28)(29)(30)(31)(32)(33)(35 36 34)(37)(38)(39)(40)(41)(42)(44 45 43)(46)(47)(48)(49)(50)(51)(53 54 52)(64 73 55)(65 74 56)(66 75 57)(67 76 58)(68 77 59)(69 78 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 31 contains 324 transformations Cycle length: 1, count: 30 Cycle length: 2, count: 12 Cycle length: 3, count: 5 Cycle length: 6, count: 2 Sample: B0r0s0t4S0c0d1e1T0 (1)(2)(3)(4)(6 5)(7)(9 8)(10)(11)(12)(13)(15 14)(16)(18 17)(19)(20)(21)(22)(24 23)(25)(27 26)(28)(29)(30)(31)(33 32)(34)(36 35)(37)(38)(39)(40)(42 41)(43)(45 44)(46)(47)(48)(49)(51 50)(52)(54 53)(64 73 55)(65 74 56)(66 75 57)(67 76 58)(69 77 60 68 78 59)(70 79 61)(72 80 63 71 81 62) Cycle factorization class 32 contains 432 transformations Cycle length: 1, count: 24 Cycle length: 2, count: 6 Cycle length: 3, count: 13 Cycle length: 6, count: 1 Sample: B0r0s0t4S0c0d1e4T0 (1)(2)(3)(4)(6 5)(8 9 7)(10)(11)(12)(13)(15 14)(17 18 16)(19)(20)(21)(22)(24 23)(26 27 25)(28)(29)(30)(31)(33 32)(35 36 34)(37)(38)(39)(40)(42 41)(44 45 43)(46)(47)(48)(49)(51 50)(53 54 52)(64 73 55)(65 74 56)(66 75 57)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 33 contains 144 transformations Cycle length: 1, count: 18 Cycle length: 3, count: 21 Sample: B0r0s0t4S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(28)(29)(30)(32 33 31)(35 36 34)(37)(38)(39)(41 42 40)(44 45 43)(46)(47)(48)(50 51 49)(53 54 52)(64 73 55)(65 74 56)(66 75 57)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 34 contains 540 transformations Cycle length: 1, count: 18 Cycle length: 2, count: 18 Cycle length: 3, count: 3 Cycle length: 6, count: 3 Sample: B0r0s0t4S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(28)(30 29)(31)(33 32)(34)(36 35)(37)(39 38)(40)(42 41)(43)(45 44)(46)(48 47)(49)(51 50)(52)(54 53)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(70 79 61)(72 80 63 71 81 62) Cycle factorization class 35 contains 648 transformations Cycle length: 1, count: 12 Cycle length: 2, count: 12 Cycle length: 3, count: 11 Cycle length: 6, count: 2 Sample: B0r0s0t4S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(28)(30 29)(31)(33 32)(35 36 34)(37)(39 38)(40)(42 41)(44 45 43)(46)(48 47)(49)(51 50)(53 54 52)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 36 contains 432 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 6 Cycle length: 3, count: 19 Cycle length: 6, count: 1 Sample: B0r0s0t4S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(28)(30 29)(32 33 31)(35 36 34)(37)(39 38)(41 42 40)(44 45 43)(46)(48 47)(50 51 49)(53 54 52)(64 73 55)(66 74 57 65 75 56)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 37 contains 729 transformations Cycle length: 1, count: 25 Cycle length: 2, count: 28 Sample: B0r0s1t1S0c0d1e1T0 (1)(2)(3)(4)(6 5)(7)(9 8)(10)(11)(12)(13)(15 14)(16)(18 17)(19)(20)(21)(22)(24 23)(25)(27 26)(28)(29)(30)(31)(33 32)(34)(36 35)(46 37)(47 38)(48 39)(49 40)(51 41)(50 42)(52 43)(54 44)(53 45)(55)(56)(57)(58)(60 59)(61)(63 62)(73 64)(74 65)(75 66)(76 67)(78 68)(77 69)(79 70)(81 71)(80 72) Cycle factorization class 38 contains 1944 transformations Cycle length: 1, count: 20 Cycle length: 2, count: 17 Cycle length: 3, count: 5 Cycle length: 6, count: 2 Sample: B0r0s1t1S0c0d1e4T0 (1)(2)(3)(4)(6 5)(8 9 7)(10)(11)(12)(13)(15 14)(17 18 16)(19)(20)(21)(22)(24 23)(26 27 25)(28)(29)(30)(31)(33 32)(35 36 34)(46 37)(47 38)(48 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(55)(56)(57)(58)(60 59)(62 63 61)(73 64)(74 65)(75 66)(76 67)(78 68)(77 69)(80 72 79 71 81 70) Cycle factorization class 39 contains 648 transformations Cycle length: 1, count: 15 Cycle length: 2, count: 6 Cycle length: 3, count: 10 Cycle length: 6, count: 4 Sample: B0r0s1t1S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(28)(29)(30)(32 33 31)(35 36 34)(46 37)(47 38)(48 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(55)(56)(57)(59 60 58)(62 63 61)(73 64)(74 65)(75 66)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 40 contains 2430 transformations Cycle length: 1, count: 15 Cycle length: 2, count: 33 Sample: B0r0s1t1S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(28)(30 29)(31)(33 32)(34)(36 35)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(52 43)(54 44)(53 45)(55)(57 56)(58)(60 59)(61)(63 62)(73 64)(75 65)(74 66)(76 67)(78 68)(77 69)(79 70)(81 71)(80 72) Cycle factorization class 41 contains 2916 transformations Cycle length: 1, count: 10 Cycle length: 2, count: 22 Cycle length: 3, count: 5 Cycle length: 6, count: 2 Sample: B0r0s1t1S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(28)(30 29)(31)(33 32)(35 36 34)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(55)(57 56)(58)(60 59)(62 63 61)(73 64)(75 65)(74 66)(76 67)(78 68)(77 69)(80 72 79 71 81 70) Cycle factorization class 42 contains 1944 transformations Cycle length: 1, count: 5 Cycle length: 2, count: 11 Cycle length: 3, count: 10 Cycle length: 6, count: 4 Sample: B0r0s1t1S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(28)(30 29)(32 33 31)(35 36 34)(46 37)(48 38)(47 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(55)(57 56)(59 60 58)(62 63 61)(73 64)(75 65)(74 66)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 43 contains 12960 transformations Cycle length: 3, count: 15 Cycle length: 6, count: 6 Sample: B0r0s1t1S0c4d4e4T0 (2 3 1)(5 6 4)(8 9 7)(11 12 10)(14 15 13)(17 18 16)(20 21 19)(23 24 22)(26 27 25)(29 30 28)(32 33 31)(35 36 34)(47 39 46 38 48 37)(50 42 49 41 51 40)(53 45 52 44 54 43)(56 57 55)(59 60 58)(62 63 61)(74 66 73 65 75 64)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 44 contains 1296 transformations Cycle length: 1, count: 16 Cycle length: 2, count: 10 Cycle length: 3, count: 11 Cycle length: 6, count: 2 Sample: B0r0s1t4S0c0d1e4T0 (1)(2)(3)(4)(6 5)(8 9 7)(10)(11)(12)(13)(15 14)(17 18 16)(19)(20)(21)(22)(24 23)(26 27 25)(28)(29)(30)(31)(33 32)(35 36 34)(46 37)(47 38)(48 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(64 73 55)(65 74 56)(66 75 57)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 45 contains 864 transformations Cycle length: 1, count: 12 Cycle length: 2, count: 3 Cycle length: 3, count: 17 Cycle length: 6, count: 2 Sample: B0r0s1t4S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(28)(29)(30)(32 33 31)(35 36 34)(46 37)(47 38)(48 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(64 73 55)(65 74 56)(66 75 57)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 46 contains 3240 transformations Cycle length: 1, count: 12 Cycle length: 2, count: 21 Cycle length: 3, count: 3 Cycle length: 6, count: 3 Sample: B0r0s1t4S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(28)(30 29)(31)(33 32)(34)(36 35)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(52 43)(54 44)(53 45)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(70 79 61)(72 80 63 71 81 62) Cycle factorization class 47 contains 3888 transformations Cycle length: 1, count: 8 Cycle length: 2, count: 14 Cycle length: 3, count: 9 Cycle length: 6, count: 3 Sample: B0r0s1t4S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(28)(30 29)(31)(33 32)(35 36 34)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 48 contains 2592 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 7 Cycle length: 3, count: 15 Cycle length: 6, count: 3 Sample: B0r0s1t4S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(28)(30 29)(32 33 31)(35 36 34)(46 37)(48 38)(47 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(64 73 55)(66 74 57 65 75 56)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 49 contains 144 transformations Cycle length: 1, count: 9 Cycle length: 3, count: 24 Sample: B0r0s4t4S0c0d4e4T0 (1)(2)(3)(5 6 4)(8 9 7)(10)(11)(12)(14 15 13)(17 18 16)(19)(20)(21)(23 24 22)(26 27 25)(37 46 28)(38 47 29)(39 48 30)(41 51 31)(42 49 32)(40 50 33)(44 54 34)(45 52 35)(43 53 36)(64 73 55)(65 74 56)(66 75 57)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 50 contains 1080 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 9 Cycle length: 3, count: 6 Cycle length: 6, count: 6 Sample: B0r0s4t4S0c1d1e1T0 (1)(3 2)(4)(6 5)(7)(9 8)(10)(12 11)(13)(15 14)(16)(18 17)(19)(21 20)(22)(24 23)(25)(27 26)(37 46 28)(39 47 30 38 48 29)(40 49 31)(42 50 33 41 51 32)(43 52 34)(45 53 36 44 54 35)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(70 79 61)(72 80 63 71 81 62) Cycle factorization class 51 contains 1296 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 6 Cycle length: 3, count: 13 Cycle length: 6, count: 4 Sample: B0r0s4t4S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(10)(12 11)(13)(15 14)(17 18 16)(19)(21 20)(22)(24 23)(26 27 25)(37 46 28)(39 47 30 38 48 29)(40 49 31)(42 50 33 41 51 32)(44 54 34)(45 52 35)(43 53 36)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 52 contains 864 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 3, count: 20 Cycle length: 6, count: 2 Sample: B0r0s4t4S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(10)(12 11)(14 15 13)(17 18 16)(19)(21 20)(23 24 22)(26 27 25)(37 46 28)(39 47 30 38 48 29)(41 51 31)(42 49 32)(40 50 33)(44 54 34)(45 52 35)(43 53 36)(64 73 55)(66 74 57 65 75 56)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 53 contains 4860 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 24 Cycle length: 3, count: 3 Cycle length: 6, count: 3 Sample: B0r1s1t1S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(19 10)(21 11)(20 12)(22 13)(24 14)(23 15)(26 18 25 17 27 16)(28)(30 29)(31)(33 32)(35 36 34)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(55)(57 56)(58)(60 59)(62 63 61)(73 64)(75 65)(74 66)(76 67)(78 68)(77 69)(80 72 79 71 81 70) Cycle factorization class 54 contains 3240 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 12 Cycle length: 3, count: 6 Cycle length: 6, count: 6 Sample: B0r1s1t1S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(19 10)(21 11)(20 12)(23 15 22 14 24 13)(26 18 25 17 27 16)(28)(30 29)(32 33 31)(35 36 34)(46 37)(48 38)(47 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(55)(57 56)(59 60 58)(62 63 61)(73 64)(75 65)(74 66)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 55 contains 75744 transformations Cycle length: 3, count: 9 Cycle length: 6, count: 9 Sample: B0r1s1t1S0c4d4e4T0 (2 3 1)(5 6 4)(8 9 7)(20 12 19 11 21 10)(23 15 22 14 24 13)(26 18 25 17 27 16)(29 30 28)(32 33 31)(35 36 34)(47 39 46 38 48 37)(50 42 49 41 51 40)(53 45 52 44 54 43)(56 57 55)(59 60 58)(62 63 61)(74 66 73 65 75 64)(77 69 76 68 78 67)(80 72 79 71 81 70) Cycle factorization class 56 contains 2916 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 16 Cycle length: 3, count: 7 Cycle length: 6, count: 4 Sample: B0r1s1t4S0c1d1e4T0 (1)(3 2)(4)(6 5)(8 9 7)(19 10)(21 11)(20 12)(22 13)(24 14)(23 15)(26 18 25 17 27 16)(28)(30 29)(31)(33 32)(35 36 34)(46 37)(48 38)(47 39)(49 40)(51 41)(50 42)(53 45 52 44 54 43)(64 73 55)(66 74 57 65 75 56)(67 76 58)(69 77 60 68 78 59)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 57 contains 3888 transformations Cycle length: 1, count: 2 Cycle length: 2, count: 8 Cycle length: 3, count: 11 Cycle length: 6, count: 5 Sample: B0r1s1t4S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(19 10)(21 11)(20 12)(23 15 22 14 24 13)(26 18 25 17 27 16)(28)(30 29)(32 33 31)(35 36 34)(46 37)(48 38)(47 39)(50 42 49 41 51 40)(53 45 52 44 54 43)(64 73 55)(66 74 57 65 75 56)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 58 contains 1296 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 4 Cycle length: 3, count: 16 Cycle length: 6, count: 4 Sample: B0r1s4t4S0c1d4e4T0 (1)(3 2)(5 6 4)(8 9 7)(19 10)(21 11)(20 12)(23 15 22 14 24 13)(26 18 25 17 27 16)(37 46 28)(39 47 30 38 48 29)(41 51 31)(42 49 32)(40 50 33)(44 54 34)(45 52 35)(43 53 36)(64 73 55)(66 74 57 65 75 56)(68 78 58)(69 76 59)(67 77 60)(71 81 61)(72 79 62)(70 80 63) Cycle factorization class 59 contains 108 transformations Cycle length: 1, count: 27 Cycle length: 2, count: 9 Cycle length: 4, count: 9 Sample: B0r0s0t0S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(28)(29)(30)(34 31)(36 33 35 32)(37)(38)(39)(43 40)(45 42 44 41)(46)(47)(48)(52 49)(54 51 53 50)(55)(56)(57)(61 58)(63 60 62 59)(64)(65)(66)(70 67)(72 69 71 68)(73)(74)(75)(79 76)(81 78 80 77) Cycle factorization class 60 contains 69984 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 4, count: 4 Cycle length: 8, count: 7 Sample: B0r0s0t0S1c0d0e1T1 (1)(10 2)(19 3)(55 7 28 4)(73 9 46 6 64 8 37 5)(11)(20 12)(56 16 29 13)(74 18 47 15 65 17 38 14)(21)(57 25 30 22)(75 27 48 24 66 26 39 23)(58 61 34 31)(76 63 52 33 67 62 43 32)(40 59 79 36 49 60 70 35)(77 81 54 51 69 71 44 41)(68 80 45 50 78 72 53 42) Cycle factorization class 61 contains 72 transformations Cycle length: 1, count: 27 Cycle length: 6, count: 9 Sample: B0r0s0t0S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(28)(29)(30)(35 32 36 33 34 31)(37)(38)(39)(44 41 45 42 43 40)(46)(47)(48)(53 50 54 51 52 49)(55)(56)(57)(62 59 63 60 61 58)(64)(65)(66)(71 68 72 69 70 67)(73)(74)(75)(80 77 81 78 79 76) Cycle factorization class 62 contains 46656 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 12, count: 6 Sample: B0r0s0t0S1c0d0e4T1 (1)(10 2)(19 3)(64 8 37 5 73 9 46 6 55 7 28 4)(11)(20 12)(65 17 38 14 74 18 47 15 56 16 29 13)(21)(66 26 39 23 75 27 48 24 57 25 30 22)(67 71 44 41 77 81 54 51 60 61 34 31)(76 72 53 42 59 79 36 49 69 62 43 32)(58 70 35 40 68 80 45 50 78 63 52 33) Cycle factorization class 63 contains 69984 transformations Cycle length: 1, count: 1 Cycle length: 4, count: 20 Sample: B0r0s0t0S1c1d0e0T1 (1)(19 3 10 2)(55 7 28 4)(64 8 37 5)(73 9 46 6)(20 21 12 11)(56 25 30 13)(65 26 39 14)(74 27 48 15)(29 22 57 16)(38 23 66 17)(47 24 75 18)(58 61 34 31)(67 62 43 32)(76 63 52 33)(40 59 70 35)(49 60 79 36)(68 71 44 41)(77 72 53 42)(50 69 80 45)(78 81 54 51) Cycle factorization class 64 contains 5184 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 18 Cycle length: 4, count: 9 Sample: B0r0s0t0S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(28)(30 29)(34 31)(36 33 35 32)(37)(39 38)(43 40)(45 42 44 41)(46)(48 47)(52 49)(54 51 53 50)(55)(57 56)(61 58)(63 60 62 59)(64)(66 65)(70 67)(72 69 71 68)(73)(75 74)(79 76)(81 78 80 77) Cycle factorization class 65 contains 209952 transformations Cycle length: 1, count: 1 Cycle length: 4, count: 6 Cycle length: 8, count: 7 Sample: B0r0s0t0S1c1d0e1T1 (1)(19 3 10 2)(55 7 28 4)(73 9 46 6 64 8 37 5)(20 21 12 11)(56 25 30 13)(74 27 48 15 65 26 39 14)(29 22 57 16)(38 23 75 18 47 24 66 17)(58 61 34 31)(76 63 52 33 67 62 43 32)(40 59 79 36 49 60 70 35)(77 81 54 51 69 71 44 41)(68 80 45 50 78 72 53 42) Cycle factorization class 66 contains 3456 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 9 Cycle length: 6, count: 9 Sample: B0r0s0t0S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(28)(30 29)(35 32 36 33 34 31)(37)(39 38)(44 41 45 42 43 40)(46)(48 47)(53 50 54 51 52 49)(55)(57 56)(62 59 63 60 61 58)(64)(66 65)(71 68 72 69 70 67)(73)(75 74)(80 77 81 78 79 76) Cycle factorization class 67 contains 139968 transformations Cycle length: 1, count: 1 Cycle length: 4, count: 2 Cycle length: 12, count: 6 Sample: B0r0s0t0S1c1d0e4T1 (1)(19 3 10 2)(64 8 37 5 73 9 46 6 55 7 28 4)(20 21 12 11)(65 26 39 14 74 27 48 15 56 25 30 13)(29 22 66 17 38 23 75 18 47 24 57 16)(67 71 44 41 77 81 54 51 60 61 34 31)(76 72 53 42 59 79 36 49 69 62 43 32)(58 70 35 40 68 80 45 50 78 63 52 33) Cycle factorization class 68 contains 72 transformations Cycle length: 2, count: 27 Cycle length: 3, count: 9 Sample: B0r0s0t0S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(29 30 28)(34 31)(35 32)(36 33)(38 39 37)(43 40)(44 41)(45 42)(47 48 46)(52 49)(53 50)(54 51)(56 57 55)(61 58)(62 59)(63 60)(65 66 64)(70 67)(71 68)(72 69)(74 75 73)(79 76)(80 77)(81 78) Cycle factorization class 69 contains 46656 transformations Cycle length: 3, count: 1 Cycle length: 4, count: 9 Cycle length: 6, count: 1 Cycle length: 12, count: 3 Sample: B0r0s0t0S1c4d0e0T1 (10 11 20 21 3 1)(19 12 2)(55 16 29 22 57 7 28 13 56 25 30 4)(64 17 38 23 66 8 37 14 65 26 39 5)(73 18 47 24 75 9 46 15 74 27 48 6)(58 61 34 31)(67 62 43 32)(76 63 52 33)(40 59 70 35)(49 60 79 36)(68 71 44 41)(77 72 53 42)(50 69 80 45)(78 81 54 51) Cycle factorization class 70 contains 216 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 9 Cycle length: 4, count: 9 Sample: B0r0s0t0S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(29 30 28)(34 31)(36 33 35 32)(38 39 37)(43 40)(45 42 44 41)(47 48 46)(52 49)(54 51 53 50)(56 57 55)(61 58)(63 60 62 59)(65 66 64)(70 67)(72 69 71 68)(74 75 73)(79 76)(81 78 80 77) Cycle factorization class 71 contains 139968 transformations Cycle length: 3, count: 1 Cycle length: 4, count: 1 Cycle length: 6, count: 1 Cycle length: 8, count: 4 Cycle length: 12, count: 1 Cycle length: 24, count: 1 Sample: B0r0s0t0S1c4d0e1T1 (10 11 20 21 3 1)(19 12 2)(55 16 29 22 57 7 28 13 56 25 30 4)(73 18 47 24 66 8 37 14 74 27 48 6 64 17 38 23 75 9 46 15 65 26 39 5)(58 61 34 31)(76 63 52 33 67 62 43 32)(40 59 79 36 49 60 70 35)(77 81 54 51 69 71 44 41)(68 80 45 50 78 72 53 42) Cycle factorization class 72 contains 373248 transformations Cycle length: 3, count: 1 Cycle length: 6, count: 1 Cycle length: 12, count: 6 Sample: B0r0s0t0S1c4d0e4T1 (10 11 20 21 3 1)(19 12 2)(64 17 38 23 75 9 46 15 56 25 30 4)(73 18 47 24 57 7 28 13 65 26 39 5)(55 16 29 22 66 8 37 14 74 27 48 6)(67 71 44 41 77 81 54 51 60 61 34 31)(76 72 53 42 59 79 36 49 69 62 43 32)(58 70 35 40 68 80 45 50 78 63 52 33) Cycle factorization class 73 contains 972 transformations Cycle length: 1, count: 21 Cycle length: 2, count: 12 Cycle length: 4, count: 9 Sample: B0r0s0t1S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(28)(29)(30)(34 31)(36 33 35 32)(37)(38)(39)(43 40)(45 42 44 41)(46)(47)(48)(52 49)(54 51 53 50)(55)(56)(57)(61 58)(63 60 62 59)(73 64)(74 65)(75 66)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 74 contains 648 transformations Cycle length: 1, count: 21 Cycle length: 2, count: 3 Cycle length: 6, count: 9 Sample: B0r0s0t1S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(28)(29)(30)(35 32 36 33 34 31)(37)(38)(39)(44 41 45 42 43 40)(46)(47)(48)(53 50 54 51 52 49)(55)(56)(57)(62 59 63 60 61 58)(73 64)(74 65)(75 66)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 75 contains 972 transformations Cycle length: 1, count: 7 Cycle length: 2, count: 37 Sample: B0r0s0t1S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(10)(12 11)(16 13)(17 14)(18 15)(19)(21 20)(25 22)(26 23)(27 24)(28)(30 29)(34 31)(35 32)(36 33)(37)(39 38)(43 40)(44 41)(45 42)(46)(48 47)(52 49)(53 50)(54 51)(55)(57 56)(61 58)(62 59)(63 60)(73 64)(75 65)(74 66)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 76 contains 2916 transformations Cycle length: 1, count: 7 Cycle length: 2, count: 19 Cycle length: 4, count: 9 Sample: B0r0s0t1S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(28)(30 29)(34 31)(36 33 35 32)(37)(39 38)(43 40)(45 42 44 41)(46)(48 47)(52 49)(54 51 53 50)(55)(57 56)(61 58)(63 60 62 59)(73 64)(75 65)(74 66)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 77 contains 1944 transformations Cycle length: 1, count: 7 Cycle length: 2, count: 10 Cycle length: 6, count: 9 Sample: B0r0s0t1S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(28)(30 29)(35 32 36 33 34 31)(37)(39 38)(44 41 45 42 43 40)(46)(48 47)(53 50 54 51 52 49)(55)(57 56)(62 59 63 60 61 58)(73 64)(75 65)(74 66)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 78 contains 648 transformations Cycle length: 2, count: 27 Cycle length: 3, count: 7 Cycle length: 6, count: 1 Sample: B0r0s0t1S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(29 30 28)(34 31)(35 32)(36 33)(38 39 37)(43 40)(44 41)(45 42)(47 48 46)(52 49)(53 50)(54 51)(56 57 55)(61 58)(62 59)(63 60)(74 66 73 65 75 64)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 79 contains 1944 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 7 Cycle length: 4, count: 9 Cycle length: 6, count: 1 Sample: B0r0s0t1S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(29 30 28)(34 31)(36 33 35 32)(38 39 37)(43 40)(45 42 44 41)(47 48 46)(52 49)(54 51 53 50)(56 57 55)(61 58)(63 60 62 59)(74 66 73 65 75 64)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 80 contains 46656 transformations Cycle length: 3, count: 7 Cycle length: 6, count: 10 Sample: B0r0s0t1S1c4d0e4T0 (2 3 1)(8 5 9 6 7 4)(11 12 10)(17 14 18 15 16 13)(20 21 19)(26 23 27 24 25 22)(29 30 28)(35 32 36 33 34 31)(38 39 37)(44 41 45 42 43 40)(47 48 46)(53 50 54 51 52 49)(56 57 55)(62 59 63 60 61 58)(74 66 73 65 75 64)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 81 contains 648 transformations Cycle length: 1, count: 18 Cycle length: 2, count: 6 Cycle length: 3, count: 3 Cycle length: 4, count: 6 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B0r0s0t4S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(28)(29)(30)(34 31)(36 33 35 32)(37)(38)(39)(43 40)(45 42 44 41)(46)(47)(48)(52 49)(54 51 53 50)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 82 contains 432 transformations Cycle length: 1, count: 18 Cycle length: 3, count: 3 Cycle length: 6, count: 9 Sample: B0r0s0t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(28)(29)(30)(35 32 36 33 34 31)(37)(38)(39)(44 41 45 42 43 40)(46)(47)(48)(53 50 54 51 52 49)(64 73 55)(65 74 56)(66 75 57)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 83 contains 648 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 24 Cycle length: 3, count: 1 Cycle length: 6, count: 4 Sample: B0r0s0t4S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(10)(12 11)(16 13)(17 14)(18 15)(19)(21 20)(25 22)(26 23)(27 24)(28)(30 29)(34 31)(35 32)(36 33)(37)(39 38)(43 40)(44 41)(45 42)(46)(48 47)(52 49)(53 50)(54 51)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 84 contains 1944 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 12 Cycle length: 3, count: 1 Cycle length: 4, count: 6 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B0r0s0t4S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(28)(30 29)(34 31)(36 33 35 32)(37)(39 38)(43 40)(45 42 44 41)(46)(48 47)(52 49)(54 51 53 50)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 85 contains 1296 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 6 Cycle length: 3, count: 1 Cycle length: 6, count: 10 Sample: B0r0s0t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(28)(30 29)(35 32 36 33 34 31)(37)(39 38)(44 41 45 42 43 40)(46)(48 47)(53 50 54 51 52 49)(64 73 55)(66 74 57 65 75 56)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 86 contains 432 transformations Cycle length: 2, count: 18 Cycle length: 3, count: 9 Cycle length: 6, count: 3 Sample: B0r0s0t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(29 30 28)(34 31)(35 32)(36 33)(38 39 37)(43 40)(44 41)(45 42)(47 48 46)(52 49)(53 50)(54 51)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 87 contains 1296 transformations Cycle length: 2, count: 6 Cycle length: 3, count: 9 Cycle length: 4, count: 6 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B0r0s0t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(29 30 28)(34 31)(36 33 35 32)(38 39 37)(43 40)(45 42 44 41)(47 48 46)(52 49)(54 51 53 50)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 88 contains 2916 transformations Cycle length: 1, count: 15 Cycle length: 2, count: 15 Cycle length: 4, count: 9 Sample: B0r0s1t1S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(28)(29)(30)(34 31)(36 33 35 32)(46 37)(47 38)(48 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(55)(56)(57)(61 58)(63 60 62 59)(73 64)(74 65)(75 66)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 89 contains 1944 transformations Cycle length: 1, count: 15 Cycle length: 2, count: 6 Cycle length: 6, count: 9 Sample: B0r0s1t1S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(28)(29)(30)(35 32 36 33 34 31)(46 37)(47 38)(48 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(55)(56)(57)(62 59 63 60 61 58)(73 64)(74 65)(75 66)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 90 contains 2916 transformations Cycle length: 1, count: 5 Cycle length: 2, count: 38 Sample: B0r0s1t1S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(10)(12 11)(16 13)(17 14)(18 15)(19)(21 20)(25 22)(26 23)(27 24)(28)(30 29)(34 31)(35 32)(36 33)(46 37)(48 38)(47 39)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(55)(57 56)(61 58)(62 59)(63 60)(73 64)(75 65)(74 66)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 91 contains 8748 transformations Cycle length: 1, count: 5 Cycle length: 2, count: 20 Cycle length: 4, count: 9 Sample: B0r0s1t1S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(28)(30 29)(34 31)(36 33 35 32)(46 37)(48 38)(47 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(55)(57 56)(61 58)(63 60 62 59)(73 64)(75 65)(74 66)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 92 contains 5832 transformations Cycle length: 1, count: 5 Cycle length: 2, count: 11 Cycle length: 6, count: 9 Sample: B0r0s1t1S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(28)(30 29)(35 32 36 33 34 31)(46 37)(48 38)(47 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(55)(57 56)(62 59 63 60 61 58)(73 64)(75 65)(74 66)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 93 contains 1944 transformations Cycle length: 2, count: 27 Cycle length: 3, count: 5 Cycle length: 6, count: 2 Sample: B0r0s1t1S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(29 30 28)(34 31)(35 32)(36 33)(47 39 46 38 48 37)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(56 57 55)(61 58)(62 59)(63 60)(74 66 73 65 75 64)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 94 contains 5832 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 5 Cycle length: 4, count: 9 Cycle length: 6, count: 2 Sample: B0r0s1t1S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(29 30 28)(34 31)(36 33 35 32)(47 39 46 38 48 37)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(56 57 55)(61 58)(63 60 62 59)(74 66 73 65 75 64)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 95 contains 46656 transformations Cycle length: 3, count: 5 Cycle length: 6, count: 11 Sample: B0r0s1t1S1c4d0e4T0 (2 3 1)(8 5 9 6 7 4)(11 12 10)(17 14 18 15 16 13)(20 21 19)(26 23 27 24 25 22)(29 30 28)(35 32 36 33 34 31)(47 39 46 38 48 37)(53 41 54 42 52 40)(49 44 50 45 51 43)(56 57 55)(62 59 63 60 61 58)(74 66 73 65 75 64)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 96 contains 3888 transformations Cycle length: 1, count: 12 Cycle length: 2, count: 9 Cycle length: 3, count: 3 Cycle length: 4, count: 6 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B0r0s1t4S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(28)(29)(30)(34 31)(36 33 35 32)(46 37)(47 38)(48 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 97 contains 2592 transformations Cycle length: 1, count: 12 Cycle length: 2, count: 3 Cycle length: 3, count: 3 Cycle length: 6, count: 9 Sample: B0r0s1t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(28)(29)(30)(35 32 36 33 34 31)(46 37)(47 38)(48 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(64 73 55)(65 74 56)(66 75 57)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 98 contains 3888 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 25 Cycle length: 3, count: 1 Cycle length: 6, count: 4 Sample: B0r0s1t4S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(10)(12 11)(16 13)(17 14)(18 15)(19)(21 20)(25 22)(26 23)(27 24)(28)(30 29)(34 31)(35 32)(36 33)(46 37)(48 38)(47 39)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 99 contains 11664 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 13 Cycle length: 3, count: 1 Cycle length: 4, count: 6 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B0r0s1t4S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(28)(30 29)(34 31)(36 33 35 32)(46 37)(48 38)(47 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 100 contains 7776 transformations Cycle length: 1, count: 4 Cycle length: 2, count: 7 Cycle length: 3, count: 1 Cycle length: 6, count: 10 Sample: B0r0s1t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(28)(30 29)(35 32 36 33 34 31)(46 37)(48 38)(47 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(64 73 55)(66 74 57 65 75 56)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 101 contains 2592 transformations Cycle length: 2, count: 18 Cycle length: 3, count: 7 Cycle length: 6, count: 4 Sample: B0r0s1t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(29 30 28)(34 31)(35 32)(36 33)(47 39 46 38 48 37)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 102 contains 7776 transformations Cycle length: 2, count: 6 Cycle length: 3, count: 7 Cycle length: 4, count: 6 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B0r0s1t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(29 30 28)(34 31)(36 33 35 32)(47 39 46 38 48 37)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 103 contains 1296 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 3 Cycle length: 3, count: 6 Cycle length: 4, count: 3 Cycle length: 6, count: 2 Cycle length: 12, count: 2 Sample: B0r0s4t4S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(37 46 28)(38 47 29)(39 48 30)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 104 contains 864 transformations Cycle length: 1, count: 9 Cycle length: 3, count: 6 Cycle length: 6, count: 9 Sample: B0r0s4t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(37 46 28)(38 47 29)(39 48 30)(44 50 36 42 52 31)(45 51 34 40 53 32)(43 49 35 41 54 33)(64 73 55)(65 74 56)(66 75 57)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 105 contains 1296 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 12 Cycle length: 3, count: 2 Cycle length: 6, count: 8 Sample: B0r0s4t4S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(10)(12 11)(16 13)(17 14)(18 15)(19)(21 20)(25 22)(26 23)(27 24)(37 46 28)(39 47 30 38 48 29)(43 49 34 40 52 31)(44 50 35 41 53 32)(45 51 36 42 54 33)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 106 contains 3888 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 6 Cycle length: 3, count: 2 Cycle length: 4, count: 3 Cycle length: 6, count: 4 Cycle length: 12, count: 2 Sample: B0r0s4t4S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(37 46 28)(39 47 30 38 48 29)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 107 contains 864 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 9 Cycle length: 6, count: 6 Sample: B0r0s4t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(38 48 28)(39 46 29)(37 47 30)(43 49 34 40 52 31)(44 50 35 41 53 32)(45 51 36 42 54 33)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 108 contains 2592 transformations Cycle length: 2, count: 3 Cycle length: 3, count: 9 Cycle length: 4, count: 3 Cycle length: 6, count: 2 Cycle length: 12, count: 2 Sample: B0r0s4t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(38 48 28)(39 46 29)(37 47 30)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 109 contains 4860 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 39 Sample: B0r1s1t1S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(19 10)(21 11)(20 12)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(28)(30 29)(34 31)(35 32)(36 33)(46 37)(48 38)(47 39)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(55)(57 56)(61 58)(62 59)(63 60)(73 64)(75 65)(74 66)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 110 contains 20412 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 21 Cycle length: 4, count: 9 Sample: B0r1s1t1S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(19 10)(21 11)(20 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(28)(30 29)(34 31)(36 33 35 32)(46 37)(48 38)(47 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(55)(57 56)(61 58)(63 60 62 59)(73 64)(75 65)(74 66)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 111 contains 13608 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 12 Cycle length: 6, count: 9 Sample: B0r1s1t1S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(28)(30 29)(35 32 36 33 34 31)(46 37)(48 38)(47 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(55)(57 56)(62 59 63 60 61 58)(73 64)(75 65)(74 66)(80 68 81 69 79 67)(76 71 77 72 78 70) Cycle factorization class 112 contains 3240 transformations Cycle length: 2, count: 27 Cycle length: 3, count: 3 Cycle length: 6, count: 3 Sample: B0r1s1t1S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(29 30 28)(34 31)(35 32)(36 33)(47 39 46 38 48 37)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(56 57 55)(61 58)(62 59)(63 60)(74 66 73 65 75 64)(79 67)(80 68)(81 69)(76 70)(77 71)(78 72) Cycle factorization class 113 contains 9720 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 3 Cycle length: 4, count: 9 Cycle length: 6, count: 3 Sample: B0r1s1t1S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(29 30 28)(34 31)(36 33 35 32)(47 39 46 38 48 37)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(56 57 55)(61 58)(63 60 62 59)(74 66 73 65 75 64)(79 67)(81 69 80 68)(76 70)(77 72 78 71) Cycle factorization class 114 contains 5832 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 12 Cycle length: 3, count: 3 Cycle length: 4, count: 6 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B0r1s1t4S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(19 10)(20 11)(21 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(28)(29)(30)(34 31)(36 33 35 32)(46 37)(47 38)(48 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 115 contains 3888 transformations Cycle length: 1, count: 6 Cycle length: 2, count: 6 Cycle length: 3, count: 3 Cycle length: 6, count: 9 Sample: B0r1s1t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(19 10)(20 11)(21 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(28)(29)(30)(35 32 36 33 34 31)(46 37)(47 38)(48 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(64 73 55)(65 74 56)(66 75 57)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 116 contains 5832 transformations Cycle length: 1, count: 2 Cycle length: 2, count: 26 Cycle length: 3, count: 1 Cycle length: 6, count: 4 Sample: B0r1s1t4S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(19 10)(21 11)(20 12)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(28)(30 29)(34 31)(35 32)(36 33)(46 37)(48 38)(47 39)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 117 contains 17496 transformations Cycle length: 1, count: 2 Cycle length: 2, count: 14 Cycle length: 3, count: 1 Cycle length: 4, count: 6 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B0r1s1t4S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(19 10)(21 11)(20 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(28)(30 29)(34 31)(36 33 35 32)(46 37)(48 38)(47 39)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 118 contains 11664 transformations Cycle length: 1, count: 2 Cycle length: 2, count: 8 Cycle length: 3, count: 1 Cycle length: 6, count: 10 Sample: B0r1s1t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(28)(30 29)(35 32 36 33 34 31)(46 37)(48 38)(47 39)(53 41 54 42 52 40)(49 44 50 45 51 43)(64 73 55)(66 74 57 65 75 56)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 119 contains 3888 transformations Cycle length: 2, count: 18 Cycle length: 3, count: 5 Cycle length: 6, count: 5 Sample: B0r1s1t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(29 30 28)(34 31)(35 32)(36 33)(47 39 46 38 48 37)(52 40)(53 41)(54 42)(49 43)(50 44)(51 45)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 120 contains 11664 transformations Cycle length: 2, count: 6 Cycle length: 3, count: 5 Cycle length: 4, count: 6 Cycle length: 6, count: 3 Cycle length: 12, count: 1 Sample: B0r1s1t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(29 30 28)(34 31)(36 33 35 32)(47 39 46 38 48 37)(52 40)(54 42 53 41)(49 43)(50 45 51 44)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 121 contains 3888 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 6 Cycle length: 3, count: 6 Cycle length: 4, count: 3 Cycle length: 6, count: 2 Cycle length: 12, count: 2 Sample: B0r1s4t4S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(19 10)(20 11)(21 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(37 46 28)(38 47 29)(39 48 30)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 122 contains 2592 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 3, count: 6 Cycle length: 6, count: 9 Sample: B0r1s4t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(19 10)(20 11)(21 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(37 46 28)(38 47 29)(39 48 30)(44 50 36 42 52 31)(45 51 34 40 53 32)(43 49 35 41 54 33)(64 73 55)(65 74 56)(66 75 57)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 123 contains 3888 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 13 Cycle length: 3, count: 2 Cycle length: 6, count: 8 Sample: B0r1s4t4S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(19 10)(21 11)(20 12)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(37 46 28)(39 47 30 38 48 29)(43 49 34 40 52 31)(44 50 35 41 53 32)(45 51 36 42 54 33)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 124 contains 11664 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 7 Cycle length: 3, count: 2 Cycle length: 4, count: 3 Cycle length: 6, count: 4 Cycle length: 12, count: 2 Sample: B0r1s4t4S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(19 10)(21 11)(20 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(37 46 28)(39 47 30 38 48 29)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 125 contains 7776 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 4 Cycle length: 3, count: 2 Cycle length: 6, count: 11 Sample: B0r1s4t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(37 46 28)(39 47 30 38 48 29)(44 50 36 42 52 31)(45 51 34 40 53 32)(43 49 35 41 54 33)(64 73 55)(66 74 57 65 75 56)(71 77 63 69 79 58)(72 78 61 67 80 59)(70 76 62 68 81 60) Cycle factorization class 126 contains 2592 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 7 Cycle length: 6, count: 7 Sample: B0r1s4t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(38 48 28)(39 46 29)(37 47 30)(43 49 34 40 52 31)(44 50 35 41 53 32)(45 51 36 42 54 33)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(71 77 62 68 80 59)(72 78 63 69 81 60) Cycle factorization class 127 contains 7776 transformations Cycle length: 2, count: 3 Cycle length: 3, count: 7 Cycle length: 4, count: 3 Cycle length: 6, count: 3 Cycle length: 12, count: 2 Sample: B0r1s4t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(38 48 28)(39 46 29)(37 47 30)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(65 75 55)(66 73 56)(64 74 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 128 contains 25920 transformations Cycle length: 3, count: 9 Cycle length: 6, count: 3 Cycle length: 12, count: 3 Sample: B0r4s4t4S1c0d0e1T0 (10 19 1)(11 20 2)(12 21 3)(16 22 7 13 25 4)(18 24 8 14 27 6 17 23 9 15 26 5)(37 46 28)(38 47 29)(39 48 30)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(65 74 56)(66 75 57)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 129 contains 119232 transformations Cycle length: 3, count: 3 Cycle length: 6, count: 6 Cycle length: 12, count: 3 Sample: B0r4s4t4S1c1d0e1T0 (10 19 1)(12 20 3 11 21 2)(16 22 7 13 25 4)(18 24 8 14 27 6 17 23 9 15 26 5)(37 46 28)(39 47 30 38 48 29)(43 49 34 40 52 31)(45 51 35 41 54 33 44 50 36 42 53 32)(64 73 55)(66 74 57 65 75 56)(70 76 61 67 79 58)(72 78 62 68 81 60 71 77 63 69 80 59) Cycle factorization class 130 contains 49248 transformations Cycle length: 9, count: 9 Sample: B0r0s0t0S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(13 17 11 14 18 12 15 16 10)(22 26 20 23 27 21 24 25 19)(31 35 29 32 36 30 33 34 28)(40 44 38 41 45 39 42 43 37)(49 53 47 50 54 48 51 52 46)(58 62 56 59 63 57 60 61 55)(67 71 65 68 72 66 69 70 64)(76 80 74 77 81 75 78 79 73) Cycle factorization class 131 contains 233280 transformations Cycle length: 9, count: 1 Cycle length: 18, count: 4 Sample: B0r0s0t0S4c0d0e4T1 (28 31 67 71 17 11 38 41 77 81 27 21 48 51 60 61 7 1)(37 32 76 72 26 12 47 42 59 79 9 19 30 49 69 62 16 2)(46 33 58 70 8 10 29 40 68 80 18 20 39 50 78 63 25 3)(64 35 13 65 44 14 74 45 23 75 54 24 57 52 6 55 34 4)(73 36 22 66 53 15 56 43 5) Cycle factorization class 132 contains 23328 transformations Cycle length: 9, count: 7 Cycle length: 18, count: 1 Sample: B0r0s0t1S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(13 17 11 14 18 12 15 16 10)(22 26 20 23 27 21 24 25 19)(31 35 29 32 36 30 33 34 28)(40 44 38 41 45 39 42 43 37)(49 53 47 50 54 48 51 52 46)(58 62 56 59 63 57 60 61 55)(76 71 74 68 81 66 78 70 73 67 80 65 77 72 75 69 79 64) Cycle factorization class 133 contains 23328 transformations Cycle length: 9, count: 5 Cycle length: 18, count: 2 Sample: B0r0s1t1S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(13 17 11 14 18 12 15 16 10)(22 26 20 23 27 21 24 25 19)(31 35 29 32 36 30 33 34 28)(49 44 47 41 54 39 51 43 46 40 53 38 50 45 48 42 52 37)(58 62 56 59 63 57 60 61 55)(76 71 74 68 81 66 78 70 73 67 80 65 77 72 75 69 79 64) Cycle factorization class 134 contains 116640 transformations Cycle length: 9, count: 3 Cycle length: 18, count: 3 Sample: B0r1s1t1S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(22 17 20 14 27 12 24 16 19 13 26 11 23 18 21 15 25 10)(31 35 29 32 36 30 33 34 28)(49 44 47 41 54 39 51 43 46 40 53 38 50 45 48 42 52 37)(58 62 56 59 63 57 60 61 55)(76 71 74 68 81 66 78 70 73 67 80 65 77 72 75 69 79 64) Cycle factorization class 135 contains 2916 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 8 Cycle length: 4, count: 14 Sample: B1r0s0t1S1c0d0e1T0 (1)(2)(3)(7 4)(9 6 8 5)(10)(11)(12)(16 13)(18 15 17 14)(19)(20)(21)(25 22)(27 24 26 23)(55 28)(56 29)(57 30)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(73 46 64 37)(74 47 65 38)(75 48 66 39)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 136 contains 3888 transformations Cycle length: 1, count: 9 Cycle length: 2, count: 3 Cycle length: 4, count: 3 Cycle length: 6, count: 5 Cycle length: 12, count: 2 Sample: B1r0s0t1S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(55 28)(56 29)(57 30)(62 32 63 33 61 31)(58 35 59 36 60 34)(73 46 64 37)(74 47 65 38)(75 48 66 39)(80 50 72 42 79 49 71 41 81 51 70 40)(76 53 68 45 78 52 67 44 77 54 69 43) Cycle factorization class 137 contains 17496 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 11 Cycle length: 4, count: 14 Sample: B1r0s0t1S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(10)(12 11)(16 13)(18 15 17 14)(19)(21 20)(25 22)(27 24 26 23)(55 28)(57 29)(56 30)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(73 46 64 37)(75 47 66 38)(74 48 65 39)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 138 contains 23328 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 6 Cycle length: 4, count: 3 Cycle length: 6, count: 5 Cycle length: 12, count: 2 Sample: B1r0s0t1S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(55 28)(57 29)(56 30)(62 32 63 33 61 31)(58 35 59 36 60 34)(73 46 64 37)(75 47 66 38)(74 48 65 39)(80 50 72 42 79 49 71 41 81 51 70 40)(76 53 68 45 78 52 67 44 77 54 69 43) Cycle factorization class 139 contains 3888 transformations Cycle length: 2, count: 15 Cycle length: 3, count: 3 Cycle length: 4, count: 6 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B1r0s0t1S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(56 30 55 29 57 28)(61 31)(62 32)(63 33)(58 34)(59 35)(60 36)(74 48 64 38 75 46 65 39 73 47 66 37)(79 49 70 40)(80 50 71 41)(81 51 72 42)(76 52 67 43)(77 53 68 44)(78 54 69 45) Cycle factorization class 140 contains 11664 transformations Cycle length: 2, count: 5 Cycle length: 3, count: 3 Cycle length: 4, count: 11 Cycle length: 6, count: 1 Cycle length: 12, count: 1 Sample: B1r0s0t1S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(56 30 55 29 57 28)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(74 48 64 38 75 46 65 39 73 47 66 37)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 141 contains 1296 transformations Cycle length: 1, count: 9 Cycle length: 6, count: 12 Sample: B1r0s0t4S1c0d0e4T0 (1)(2)(3)(8 5 9 6 7 4)(10)(11)(12)(17 14 18 15 16 13)(19)(20)(21)(26 23 27 24 25 22)(64 37 73 46 55 28)(65 38 74 47 56 29)(66 39 75 48 57 30)(71 41 81 51 61 31)(72 42 79 49 62 32)(70 40 80 50 63 33)(67 44 77 54 60 34)(68 45 78 52 58 35)(69 43 76 53 59 36) Cycle factorization class 142 contains 7776 transformations Cycle length: 1, count: 3 Cycle length: 2, count: 3 Cycle length: 6, count: 12 Sample: B1r0s0t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(10)(12 11)(17 14 18 15 16 13)(19)(21 20)(26 23 27 24 25 22)(64 37 73 46 55 28)(66 38 75 47 57 29)(65 39 74 48 56 30)(71 41 81 51 61 31)(72 42 79 49 62 32)(70 40 80 50 63 33)(67 44 77 54 60 34)(68 45 78 52 58 35)(69 43 76 53 59 36) Cycle factorization class 143 contains 2592 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 3 Cycle length: 6, count: 9 Sample: B1r0s0t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(11 12 10)(16 13)(17 14)(18 15)(20 21 19)(25 22)(26 23)(27 24)(65 39 73 47 57 28)(66 37 74 48 55 29)(64 38 75 46 56 30)(70 40 79 49 61 31)(71 41 80 50 62 32)(72 42 81 51 63 33)(67 43 76 52 58 34)(68 44 77 53 59 35)(69 45 78 54 60 36) Cycle factorization class 144 contains 7776 transformations Cycle length: 2, count: 3 Cycle length: 3, count: 3 Cycle length: 4, count: 3 Cycle length: 6, count: 5 Cycle length: 12, count: 2 Sample: B1r0s0t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(11 12 10)(16 13)(18 15 17 14)(20 21 19)(25 22)(27 24 26 23)(65 39 73 47 57 28)(66 37 74 48 55 29)(64 38 75 46 56 30)(70 40 79 49 61 31)(72 42 80 50 63 33 71 41 81 51 62 32)(67 43 76 52 58 34)(68 45 78 53 59 36 69 44 77 54 60 35) Cycle factorization class 145 contains 2916 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 40 Sample: B1r1s0t0S1c1d0e0T0 (1)(3 2)(7 4)(8 5)(9 6)(19 10)(21 11)(20 12)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(55 28)(57 29)(56 30)(61 31)(62 32)(63 33)(58 34)(59 35)(60 36)(64 37)(66 38)(65 39)(70 40)(71 41)(72 42)(67 43)(68 44)(69 45)(73 46)(75 47)(74 48)(79 49)(80 50)(81 51)(76 52)(77 53)(78 54) Cycle factorization class 146 contains 17496 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 22 Cycle length: 4, count: 9 Sample: B1r1s0t0S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(19 10)(21 11)(20 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(55 28)(57 29)(56 30)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(64 37)(66 38)(65 39)(70 40)(72 42 71 41)(67 43)(68 45 69 44)(73 46)(75 47)(74 48)(79 49)(81 51 80 50)(76 52)(77 54 78 53) Cycle factorization class 147 contains 11664 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 13 Cycle length: 6, count: 9 Sample: B1r1s0t0S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(55 28)(57 29)(56 30)(62 32 63 33 61 31)(58 35 59 36 60 34)(64 37)(66 38)(65 39)(71 41 72 42 70 40)(67 44 68 45 69 43)(73 46)(75 47)(74 48)(80 50 81 51 79 49)(76 53 77 54 78 52) Cycle factorization class 148 contains 3888 transformations Cycle length: 2, count: 27 Cycle length: 3, count: 1 Cycle length: 6, count: 4 Sample: B1r1s0t0S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(56 30 55 29 57 28)(61 31)(62 32)(63 33)(58 34)(59 35)(60 36)(65 39 64 38 66 37)(70 40)(71 41)(72 42)(67 43)(68 44)(69 45)(74 48 73 47 75 46)(79 49)(80 50)(81 51)(76 52)(77 53)(78 54) Cycle factorization class 149 contains 11664 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 1 Cycle length: 4, count: 9 Cycle length: 6, count: 4 Sample: B1r1s0t0S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(56 30 55 29 57 28)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(65 39 64 38 66 37)(70 40)(72 42 71 41)(67 43)(68 45 69 44)(74 48 73 47 75 46)(79 49)(81 51 80 50)(76 52)(77 54 78 53) Cycle factorization class 150 contains 93312 transformations Cycle length: 3, count: 1 Cycle length: 6, count: 13 Sample: B1r1s0t0S1c4d0e4T0 (2 3 1)(8 5 9 6 7 4)(20 12 19 11 21 10)(26 14 27 15 25 13)(22 17 23 18 24 16)(56 30 55 29 57 28)(62 32 63 33 61 31)(58 35 59 36 60 34)(65 39 64 38 66 37)(71 41 72 42 70 40)(67 44 68 45 69 43)(74 48 73 47 75 46)(80 50 81 51 79 49)(76 53 77 54 78 52) Cycle factorization class 151 contains 26244 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 12 Cycle length: 4, count: 14 Sample: B1r1s0t1S1c1d0e1T0 (1)(3 2)(7 4)(9 6 8 5)(19 10)(21 11)(20 12)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(55 28)(57 29)(56 30)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(73 46 64 37)(75 47 66 38)(74 48 65 39)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 152 contains 34992 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 7 Cycle length: 4, count: 3 Cycle length: 6, count: 5 Cycle length: 12, count: 2 Sample: B1r1s0t1S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(55 28)(57 29)(56 30)(62 32 63 33 61 31)(58 35 59 36 60 34)(73 46 64 37)(75 47 66 38)(74 48 65 39)(80 50 72 42 79 49 71 41 81 51 70 40)(76 53 68 45 78 52 67 44 77 54 69 43) Cycle factorization class 153 contains 11664 transformations Cycle length: 2, count: 15 Cycle length: 3, count: 1 Cycle length: 4, count: 6 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B1r1s0t1S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(56 30 55 29 57 28)(61 31)(62 32)(63 33)(58 34)(59 35)(60 36)(74 48 64 38 75 46 65 39 73 47 66 37)(79 49 70 40)(80 50 71 41)(81 51 72 42)(76 52 67 43)(77 53 68 44)(78 54 69 45) Cycle factorization class 154 contains 34992 transformations Cycle length: 2, count: 5 Cycle length: 3, count: 1 Cycle length: 4, count: 11 Cycle length: 6, count: 2 Cycle length: 12, count: 1 Sample: B1r1s0t1S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(56 30 55 29 57 28)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(74 48 64 38 75 46 65 39 73 47 66 37)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 155 contains 93312 transformations Cycle length: 3, count: 1 Cycle length: 6, count: 7 Cycle length: 12, count: 3 Sample: B1r1s0t1S1c4d0e4T0 (2 3 1)(8 5 9 6 7 4)(20 12 19 11 21 10)(26 14 27 15 25 13)(22 17 23 18 24 16)(56 30 55 29 57 28)(62 32 63 33 61 31)(58 35 59 36 60 34)(74 48 64 38 75 46 65 39 73 47 66 37)(80 50 72 42 79 49 71 41 81 51 70 40)(76 53 68 45 78 52 67 44 77 54 69 43) Cycle factorization class 156 contains 11664 transformations Cycle length: 1, count: 1 Cycle length: 2, count: 4 Cycle length: 6, count: 12 Sample: B1r1s0t4S1c1d0e4T0 (1)(3 2)(8 5 9 6 7 4)(19 10)(21 11)(20 12)(26 14 27 15 25 13)(22 17 23 18 24 16)(64 37 73 46 55 28)(66 38 75 47 57 29)(65 39 74 48 56 30)(71 41 81 51 61 31)(72 42 79 49 62 32)(70 40 80 50 63 33)(67 44 77 54 60 34)(68 45 78 52 58 35)(69 43 76 53 59 36) Cycle factorization class 157 contains 7776 transformations Cycle length: 2, count: 9 Cycle length: 3, count: 1 Cycle length: 6, count: 10 Sample: B1r1s0t4S1c4d0e0T0 (2 3 1)(7 4)(8 5)(9 6)(20 12 19 11 21 10)(25 13)(26 14)(27 15)(22 16)(23 17)(24 18)(65 39 73 47 57 28)(66 37 74 48 55 29)(64 38 75 46 56 30)(70 40 79 49 61 31)(71 41 80 50 62 32)(72 42 81 51 63 33)(67 43 76 52 58 34)(68 44 77 53 59 35)(69 45 78 54 60 36) Cycle factorization class 158 contains 23328 transformations Cycle length: 2, count: 3 Cycle length: 3, count: 1 Cycle length: 4, count: 3 Cycle length: 6, count: 6 Cycle length: 12, count: 2 Sample: B1r1s0t4S1c4d0e1T0 (2 3 1)(7 4)(9 6 8 5)(20 12 19 11 21 10)(25 13)(27 15 26 14)(22 16)(23 18 24 17)(65 39 73 47 57 28)(66 37 74 48 55 29)(64 38 75 46 56 30)(70 40 79 49 61 31)(72 42 80 50 63 33 71 41 81 51 62 32)(67 43 76 52 58 34)(68 45 78 53 59 36 69 44 77 54 60 35) Cycle factorization class 159 contains 1296 transformations Cycle length: 2, count: 18 Cycle length: 3, count: 3 Cycle length: 6, count: 6 Sample: B1r4s0t0S1c4d0e0T0 (11 21 1)(12 19 2)(10 20 3)(16 22 7 13 25 4)(17 23 8 14 26 5)(18 24 9 15 27 6)(56 30 55 29 57 28)(61 31)(62 32)(63 33)(58 34)(59 35)(60 36)(65 39 64 38 66 37)(70 40)(71 41)(72 42)(67 43)(68 44)(69 45)(74 48 73 47 75 46)(79 49)(80 50)(81 51)(76 52)(77 53)(78 54) Cycle factorization class 160 contains 7776 transformations Cycle length: 2, count: 6 Cycle length: 3, count: 3 Cycle length: 4, count: 6 Cycle length: 6, count: 4 Cycle length: 12, count: 1 Sample: B1r4s0t0S1c4d0e1T0 (11 21 1)(12 19 2)(10 20 3)(16 22 7 13 25 4)(18 24 8 14 27 6 17 23 9 15 26 5)(56 30 55 29 57 28)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(65 39 64 38 66 37)(70 40)(72 42 71 41)(67 43)(68 45 69 44)(74 48 73 47 75 46)(79 49)(81 51 80 50)(76 52)(77 54 78 53) Cycle factorization class 161 contains 11664 transformations Cycle length: 2, count: 2 Cycle length: 3, count: 3 Cycle length: 4, count: 8 Cycle length: 6, count: 2 Cycle length: 12, count: 2 Sample: B1r4s0t1S1c4d0e1T0 (11 21 1)(12 19 2)(10 20 3)(16 22 7 13 25 4)(18 24 8 14 27 6 17 23 9 15 26 5)(56 30 55 29 57 28)(61 31)(63 33 62 32)(58 34)(59 36 60 35)(74 48 64 38 75 46 65 39 73 47 66 37)(79 49 70 40)(81 51 71 41)(80 50 72 42)(76 52 67 43)(77 54 69 44)(78 53 68 45) Cycle factorization class 162 contains 46656 transformations Cycle length: 9, count: 3 Cycle length: 18, count: 1 Cycle length: 36, count: 1 Sample: B1r0s0t1S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(13 17 11 14 18 12 15 16 10)(22 26 20 23 27 21 24 25 19)(58 35 56 32 63 30 60 34 55 31 62 29 59 36 57 33 61 28)(76 53 65 41 81 48 69 43 73 49 71 38 77 54 66 42 79 46 67 44 74 50 72 39 78 52 64 40 80 47 68 45 75 51 70 37) Cycle factorization class 163 contains 46656 transformations Cycle length: 9, count: 1 Cycle length: 18, count: 2 Cycle length: 36, count: 1 Sample: B1r1s0t1S4c0d0e4T0 (4 8 2 5 9 3 6 7 1)(22 17 20 14 27 12 24 16 19 13 26 11 23 18 21 15 25 10)(58 35 56 32 63 30 60 34 55 31 62 29 59 36 57 33 61 28)(76 53 65 41 81 48 69 43 73 49 71 38 77 54 66 42 79 46 67 44 74 50 72 39 78 52 64 40 80 47 68 45 75 51 70 37) Totally processed 3359232 transformations Execution time: 28 seconds