---
tag: Q26QESPQKC
kind: concept
name: Almost simple group
sources:
  - wikipedia: en:25027899@r1360609638
    locator: Almost simple group
    note: adopted
    mention: wikipedia://en/25027899
    sections: [Summary]
same_as:
  wikidata: Q4734006
  wikipedia: Almost simple group
inventory: [A8KA514HWP]
---

## Summary

In mathematics, a group is said to be **almost simple** if it contains a non-[[abelian|071DDFVG4J]] [[simple group|0C093D1T4M]] and is contained within the [[automorphism group|0CWXCWP0Y0]] of that simple group – that is, if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group $A$ is almost simple if there is a (non-abelian) simple group *S* such that $S \leq A \leq \operatorname{Aut}(S)$, where the inclusion of $S$ in $\mathrm{Aut}(S)$ is the action by conjugation, which is faithful since $S$ has a trivial [[center|0DZ93493VN]].