Let $\displaystyle p $ & $\displaystyle q$ be primes with $\displaystyle q<p$ and suppose $\displaystyle G$ is a group of order$\displaystyle p^2q $. Suppose that $\displaystyle G$ has unique subgroup of order $\displaystyle q$. Prove that $\displaystyle G$ is abelian stating any theorems you use...

I'm thinking I have to use some form of Sylows theorem to show that $\displaystyle G$ is a direct sum of p-groups and hence Abelian but no idea how (or even if that is the tactic)!!

Any help appreciated...