Homomorphisms from a $p$-group to $\mathbb{F}_p$

Question

I'm doing a problem on group cohomology and have reduced it to the following: if $P$ is a $p$-group then $\textrm{Hom}(P,\mathbb{F}_p) \simeq P/\Phi(P)$ where $\Phi(P)$ is the Frattini subgroup of $P$. I know any homomorphism from $P \to \mathbb{F}_p$ is uniquely determined by a maximal subgroup of $P$. Also its easy to see $\textrm{Hom}(P/[P,P],\mathbb{F}_p) \simeq \textrm{Hom}(P,\mathbb{F}_p)$, so this may help given that $\Phi(P) = P^p[P,P]$. But I'm not particularly sure how to proceed. Any thoughts? Thanks.