Number of orbits under automorphism group

Definition
Let $$G$$ be a group. The number of orbits under automorphism group or number of automorphism classes of $$G$$ is the number of orbits of the set $$G$$ under the action of the automorphism group $$\operatorname{Aut}(G)$$.

Facts

 * Number of orbits of irreducible representations equals number of orbits under automorphism group (true for a finite group and a splitting field thereof)