Coprime automorphism group

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Definition

Let G be a finite group. A subgroup H of the automorphism group \operatorname{Aut}(G) is termed a coprime automorphism group of G if the orders of G and H are relatively prime.

Note that the whole group \operatorname{Aut}(G) is very rarely coprime to G in order. Further information: Coprime automorphism group implies cyclic with order a cyclicity-forcing number