The profinite genus of the groups ${\mathbb{Z}}^n⋊C_{p^2}$

A formula is given for the profinite genus of groups of the form ${\mathbb{Z}}^n⋊C_{p^2}$, completing the calculation of the size of the genus of semidirect products of the form ${\mathbb{Z}}^n⋊G$ where $G$ is a finite $p$-group of finite integral representation type.