It has been mentioned that you started the counting on the number of essentially different 5x2 grids. Did you get the number? I have started the counting on my own, after first confirming the numbers 49 for 3x2 and 1673187 for 4x2, but I understand 5x2 will take time. I use the same method as you, counting fixed grids for one element inside each conjugacy class of legal operations. I have no idea about when the counting can complete - the current implementation will take weeks, but there are shortcuts I have discovered but not implemented yet.

By dividing the number of grids by the number of legal operations, we get an estimated minimal limit of essentially different grids which is pretty close to the exact answer for dimensions greater than 3x2.

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`Dim #diff.grids Estimated min Rel.err.`

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2x2 T 2 0,09375 -95,3%

2x2 N 3 0,1875 -93,8%

3x2 49 11,33333333 -76,9%

4x2 1673187 1633552 -2,37%

5x2 n/a 4743929631232717 n/a

3x3 T 5472730538 5472447995 -0,00516%

3x3 N 10945437157 10944895989 -0,00494%

3x4 n/a 6,56848258e+28 n/a

3x5 n/a 2,7733e+59(*) n/a

4x4 n/a 4,4916e+71(*) n/a

4x5 n/a 2,7456e+138(*) n/a

5x5 n/a 3,1560e+258(*) n/a

T = Transposing included

N = No transposing included

(*) based on estimated number of grids

This should give an idea about what to expect from 5x2.