On special type of p-group of class two Let $G$ be a finite $p$-group of class two and  $T$ be the minimal set of generators of $G$. Also let
$G=\langle a, b, x_{1},..., x_{n}\rangle$ such that $|a|=|b|=p^n$,  $a,b\in T$,   $x_{1},..., x_{n}\in (T\cap Z(G))$ and $|x_{i}|< p^n$ for $i$.
Then do can say that
$$G=\langle a, b\rangle\times \langle x_{1},...,x_{n}\rangle?$$
 I think this is true.
Thank you 

I think the answer is NO. The best one can get is that $G$ is a quotient of $\langle a,b\rangle \times \langle x_1,\cdots, x_n\rangle$, that is $G$ is a central product of the two subgroups.
