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 $\mathrm{conj}(G)$.

Since conjugation by fixed $g\in G$ is an automorphism of $G$, 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.**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by David Roe on 2020-10-13 18:18:47

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**History:**(expand/hide all)

- 2020-10-13 18:18:47 by David Roe (Reviewed)
- 2019-05-23 17:33:39 by John Jones
- 2018-07-09 22:28:56 by John Jones (Reviewed)

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