Example

In S₄ the permutations (in list notation) g = [2, 1, 4, 3] and h = [3, 4, 1, 2] are conjugate, since both have the cycle structure 2, 2:

g = (1,2)(3,4) and h = (1,3)(2,4).

A permutation k such that kgk^-1 = h is k = [1, 3, 2, 4]. In disjoint cycles notation this is (2,3).