Let $G$ be a group. An **automorphism of $G$** is a group isomorphism $f:G\rightarrow G$.

The set ${\rm Aut}(G)$ of all automorphisms of $G$ is a group under composition of maps.

Let $S_n$ be the symmetric group on $n\ge 1$ objects and let $C_n$ be any cyclic group of order $n\ge 1$

Which of the following are **TRUE**?

Select **ALL** that apply.