There is a surjective homomorphism from $G$ to $G'$. Let $C$ denote the conjugacy class of element $x$ in $G$, $C'$ the conjugacy class of the image of $x$ in $G'$. Prove the order of $C'$ divides the order of $C$.
So far, using the class equation I can observe that $|C|$ divides $|G|$ and $|C'|$ divides $|G'|$, and it's also obvious that the homomorphism maps $C$ surjectively to $C'$. But I can't quite piece it all together.
Any help appreciated.