Prove the center of $G$ cannot have order $p^{n-1}$ Let $p$ be a prime, let $n>2$ be an integer, and let $G$ be a nonabelian group of order $p^n$. Prove the center of G cannot have order $p^{n-1}$.

Honestly I have no idea where to start. Perhaps prove this by contradiction?

$G/Z(G)$ has order $p$; so it must be ______? But if $G/Z(G)$ is ______ then it is trivial.
