PermutationReplace
PermutationReplace[expr, perm] replaces each part in expr by its image under the permutation perm.
PermutationReplace[expr, gr]returns the list of images of expr under all elements of the permutation group gr.
Examples
PermutationReplace[{a, b, c}, Cycles[{{1, 2, 3}}]]Please visit the official Wolfram Language Reference for more details.