Coprime automorphism group

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