---
tag: 0K1SCPBNKJ
kind: concept
name: Automorphism group
msc: [20F28]
sources:
  - url: https://en.wikipedia.org/wiki/Automorphism_group
    locator: lead section
same_as:
  wikidata: Q60790315
  wikipedia: Automorphism group
---

## Summary

The automorphism group of a group $G$ is the group of all isomorphisms from $G$ to itself, with composition as the operation.
It describes the symmetries of the structure of $G$.