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2

We assume you've already read about Cayley's theorem which others also mentioned in their comments. Let's pick up a group, for example Klein 4-group, $K_4$, and to be consistent with each other let's pick up the table of multiplication that is represented in its wikipedia page (https://en.wikipedia.org/wiki/Klein_four-group). I also prefer to replace the ...

1

An answer written by MuthuVeerappanR in the forum of Project-Euler: Clear["Global`*"]; Tp = Cycles[{{9, 5, 17, 13}, {10, 6, 18, 14}, {1, 2, 4, 3}}]; Rt = Cycles[{{13, 14, 16, 15}, {10, 2, 19, 22}, {12, 4, 17, 24}}]; Fr = Cycles[{{9, 10, 12, 11}, {3, 13, 22, 8}, {4, 15, 21, 6}}]; Dn = Cycles[{{21, 22, 24, 23}, {11, 15, 19, 7}, {12, 16, 20, 8}}]; Lt = Cycles[{...

5

I think some of the rotations must be corrected: rot1 = Cycles[{{1, 2, 4, 3}, {5, 24, 9, 7}, {6, 23, 10, 8}}]; rot2 = Cycles[{{21, 22, 24, 23}, {1, 11, 20, 10}, {2, 5, 19, 16}}]; rot3 = Cycles[{{11, 5, 6, 12}, {1, 7, 17, 21}, {3, 13, 19, 23}}]; rot4 = Cycles[{{7, 8, 14, 13}, {3, 9, 18, 12}, {4, 15, 17, 6}}]; rot5 = Cycles[{{10, 16, 15, 9}, {2, 22, 18, 8}, {...

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