I'm trying to teach myself with Sylow Theorems and conjugacy classes. I was reading a proof which involved automorphism and conjugacy class in the group and this was one of the step to the proof.
The statement I'm trying to "If $C$ is a conjugacy class of a group $G$ and $f$ is an automorphism of $G$, prove that $f(C)$ is also a conjugacy class of $G$" The proof consists of assuming $C$ is a conjugacy class of an element in $G$ and since $f$ is an automorphism which is also an isomorphism.
"every isomorphic group has a conjugacy class for the given function."
Why is this a true statement? What would be the steps to prove it?