Inner automorphism of a group (reviewed)

If $G$ is a group and $g\in G$, then the function $\phi_g:G\to G$ given by conjugation by $g$ $\phi_g(x) = gxg^{-1}$ is an automorphism of $G$ called an inner automorphism.

The set of inner automorphisms $\mathrm{Inn}(G)$ is a subgroup of $\Aut(G)$, and $\mathrm{Inn}(G) \cong G/Z(G)$ where $Z(G)$ is the center of $G$.