---
type: "problem"
title: "Groups with 3 conjugacy classes"
slug: "groups-with-3-conjugacy-classes"
author: "ancient-tree"
tags: ["conjugacy classes", "group"]
difficulty: 51
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Let $G$ be a group with 3 conjugacy classes. Show that $G\cong \mathbb{Z}/3\mathbb{Z}$ or $G\cong S_3$.