SCHWEITZER 1952 Problem 5

Let $G$ be anon-commutative group. Consider all the one-to-one mappings $a\rightarrow a'$ of $G$ onto itself such that $(ab)'=b'a'$ (i.e. the anti-automorphisms of $G$ ). Prove that this mappings together with the automorphisms of $G$ constitute a group which contains the group of the automorphisms of $G$ as direct factor.