Outer automorphism group (reviewed)

If $G$ is a group, its inner automorphism group is a normal subgroup of the full automorphism group. Then, the outer automorphism group of $G$ is \[ \mathrm{Out}(G) = \Aut(G)/\mathrm{Inn}(G).\]

Note that the term outer automorphism is often used to mean any automorphism of a group $G$ which is not an inner automorphism. In this case, the nontrivial elements of the outer automorphism group are cosets of outer automorphisms.