Let $a$ belong to a group $G$ and let $|a|$ be finite. Let $ø_a(x) = axa^{-1}$ for elements $x$ in $G$. Show that the order of $ø_a$ divides the order of $a$. Exhibit an element from a group for which $1 < |ø_a| < |a|$.
Since this is technically homework I'm not expecting a complete proof, but an idea of where to start would be greatly appreciated.