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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 $G$, and the set of conjugacy classes is denoted by $G^\natural$.

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 David Roe on 2020-10-13 18:18:47
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