Editing Complete group (section)

== Examples ==
As an example, all the [[symmetric group]]s, {{math|S{{sub|''n''}}}}, are complete except when {{math|''n'' ∈ {2, 6}}}. For the case {{math|''n'' {{=}} 2}}, the group has a non-trivial center, while for the case {{math|''n'' {{=}} 6}}, there is an [[automorphisms of the symmetric and alternating groups#exceptional outer automorphism|outer automorphism]].

The automorphism group of a [[simple group]] is an [[almost simple group]]; for a non-[[abelian group|abelian]] simple group {{math|''G''}}, the automorphism group of {{math|''G''}} is complete.