---
tag: 0DEBXAJ5SA
kind: concept
name: Conjugacy class
msc: ["20E45"]
sources:
  - url: https://en.wikipedia.org/wiki/Conjugacy_class
    locator: Definition
same_as:
  wikidata: Q1353233
  wikipedia: Conjugacy class
---

## Summary

The conjugacy class of an element $a$ of a group $G$ is the set of all elements $gag^{-1}$ with $g \in G$.
The conjugacy classes partition the group.