This is a follow up to this question
Let $G_{1}$ and $G_{2}$ be two finite UCS p-groups with the following conditions:
1- $\vert G_{1}\vert=\vert G_{2}\vert=p^{2n}$;
2- $\Phi(G_{1})\cong\Phi(G_{2})\cong\underbrace{\mathbb{Z}_{p}\times\mathbb{Z}_{p}\times\dots\times\mathbb{Z}_{p}}_{n\,\,times}$;
3- $G_{1}$ and $G_{2}$ have the same number of minimal subgroups.
Can we prove that $G_{1}\cong G_{2}$? Is there any counterexamples?
