Let $p$ be a prime number and $n$ an integer such that $p\geq n$. Let $P(n)$ denotes the  number  of  partitions of $n$. Can we conclude from Theorem 1.1 and Theorem 1.3 in the reference [FINITE_p-GROUPS_OF_MAXIMAL_CLASS_AND_EXPONENT_p](https://www.researchgate.net/publication/337221031_ON_A_SPECIAL_CLASS_OF_FINITE_p-GROUPS_OF_MAXIMAL_CLASS_AND_EXPONENT_p), that the  number of  isomorphism  classes  of  splits  extensions of $( \mathbb{Z} / p \mathbb{Z} )^n$ by $\mathbb{Z} / p \mathbb{Z} $ with a non abelian middle groups is $P(n)-1$ ?. Does the subgroup $( \mathbb{Z} / p \mathbb{Z} )^n$ should be here characteristic in $(\mathbb{Z}/p\mathbb{Z})^{n}\rtimes \mathbb{Z}/p\mathbb{Z}$ ?.  


Any help would be appreciated so much. Thank you all.