# Extended automorphism group

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Let $G$ be a group. The extended automorphism group of $G$ is the group comprising all the automorphisms and anti-automorphisms of $G$. An anti-automorphism is a map $\varphi:G \to G$ such that $\varphi(gh) = \varphi(h)\varphi(g)$ for all $g,h \in G$.