Cycle_Decomposition_of_Conjugate_v2

Let $S_n$ denote the symmetric group on $n$ letters. Let $\pi, \rho \in S_n$. The cycle decomposition of the permutation $\pi \rho \pi^{-1}$ can be obtained from that of $\rho$ by replacing each $i$ in the cycle decomposition of $\rho$ with $\map \pi i$.