Almost simple group
In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group – that is, if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group A {\displaystyle A} is almost simple if there is a (non-abelian) simple group S such that S ≤ A ≤ Aut ( S ) {\displaystyle S\leq A\leq \operatorname {Aut} (S)} , where the inclusion of S {\displaystyle S} in A u t ( S ) {\displaystyle \mathrm {Aut} (S)} is the action by conjugation, which is faithful since S {\displaystyle S} has a trivial center.