Autjugacy class (reviewed)

If $G$ is a group and $x \in G$, the autjugacy class of $x$ is the orbit of $x$ under the action of the automorphism group, namely $\{\varphi(x) : \varphi \in \operatorname{Aut}(G)\}$. Any autjugacy class is a disjoint union of conjugacy classes, each of the same size and order.