Define a fusion class of a finite group G to be a set $F(x)=\{\phi(x):\phi\in$ Aut$(G)\}$ for some $x\in G$.
Now, suppose $G$ is a noncyclic group. I want to say something about the order of each nontrivial fusion class of $G$.
I suppose I am just getting hung up on the fusion class versus the conjugacy class. I know the difference between them (conjugacy class is over inner automorphisms whereas the fusion class is over all automorphisms) but when I am computing $|F_i|$, for each $i$, would I still consider $|G:C_g|$, where $C_g$ is the centralizer? So would the order of each fusions class, since $G$ is noncyclic, just be $|G|$?
I feel like I am just overlooking something obvious.