Presentation of a non-abelian group of order $p^4$ such that ${G}/{\Phi(G)}\cong \Bbb{Z}_p\times \Bbb{Z}_p$

Question

Let $G$ be a finite non-abelian $p$-group of order $p^4$ and $\frac{G}{\Phi(G)}\cong \Bbb{Z}_p\times \Bbb{Z}_p$, where $p$ is a prime. What is the presentation(s) of $G$?(If $G$ exixsts).

Thanks for any answer or comment!

Answer 1

One such example is $$\langle a,b,c,d \mid a^p=b^p=1,[a,b]=c,[a,c]=[b,c]=d, [a,d]=[b,d]=1 \rangle,$$ which works for any prime $p$, but there are other groups with this property.

Added later: For some reason I looked for an example with nilpotency class $3$, but there are examples with class $2$, such as $$\langle a,b,c \mid a^{p^2}=b^p=c^p=1, [a,b]=c, [a,c]=[b,c]=1 \rangle.$$