Replaces each point in an expression by its image under a permutation or list of permutations
PermutationReplace[expr, perm]
PermutationReplace[expr, gr]
PermutationReplace[4, Cycles[{}]]
→ 4PermutationReplace[4, Cycles[{{2, 3, 4, 6}}]]
→ 6PermutationReplace[Cycles[{{1, 4}, {2, 5, 6, 3}}], Cycles[{{2, 3, 5, 1, 4, 6}}]]
→ Cycles[{{1, 4}, {2, 5, 6, 3}}]