---
type: "concept"
title: "Conjugacy class"
slug: "conjugacy-class"
language: "en"
translationGroupId: "cmqw3hgqg0003s0016oqfl7vv"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

Let $G$ be a [[Group|group]]. The conjugacy class of an element $a\in G$ is the set of all elements [[Conjugate elements|conjugate]] to $a$:
$$\{gag^{-1}:g\in G\}$$