If $G$ is a group and $x\in G$, the **conjugacy class** of $x$ is the set $\{gxg^{-1}\mid g\in G\}$. These sets partition $G$.

Since conjugation by fixed $g\in G$ is an automorphism of a $G$, all conjugate elements have the same order in the group. If $G\leq S_n$, then all elements in the conjugacy class of an element have the same cycle type.

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- Last edited by John Jones on 2018-07-09 22:28:56

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