For an integer in expr present in the cycles of the permutation perm, the image is the integer to the right of , or the first integer of the cycle if is the last one. For an integer not present in the cycles of perm, the image is itself.
If g is a permutation object in expr, then the action is understood as right conjugation: PermutationProduct[InversePermutation[perm], g, perm]. This is equivalent to replacing the points in the cycles of g by their images under perm.
When applied to a permutation group expr, PermutationReplace operates on each individual generator, returning the same abstract group but acting on different points.
Both arguments are independently listable. If both arguments are lists then the second argument is threaded first.