---
tag: 91JDYBHHF1
kind: concept
name: Metacyclic group
aliases: [meta-cyclic-group, metacyclic]
sources:
  - wikipedia: en:7515561@r1334869561
    locator: Metacyclic group
    note: adopted
    mention: wikipedia://en/7515561
    sections: [Summary]
same_as:
  wikidata: Q6822469
  wikipedia: Metacyclic group
inventory: [EJADFVKKQF]
---

## Summary

In group theory, a **metacyclic group** is an extension of a [[cyclic group|0B85Q41RP6]] by a cyclic group. Equivalently, a metacyclic group is a group $G$ having a cyclic [[normal subgroup|0CB0DX5BVV]] $N$, such that the [[quotient|0KYX2N69J0]] $G/N$ is also cyclic.