Groups of prime squared order 
I have done part $a$ and $b$, stuck on $c$. I don't know what to do here. I know that since $G$ has order $p^2$, any  element must have order $1, p$ or $p^2$ so any generator must have one of those orders, but I don't know how to reason any further..

So if you have no elements of order $p^2$, then all your elements have order $p$. Hence every group you have is cyclic of order $p$. Since they meet at the identity, there is a total of $x(p-1)+1=p^2$ elements. $x$ is what?
