Character codegrees of maximal class p-groups

Abstract

Let $G$ be a $p$-group and let $\chi$ be an irreducible character of $G$. The codegree of $\chi$ is given by $|G:\text{ker}(\chi )|/\chi (1)$. If $G$ is a maximal class $p$-group that is normally monomial or has at most three character degrees then the codegrees of $G$ are consecutive powers of $p$. If $|G|=p^n$ and $G$ has consecutive $p$-power codegrees up to $p^{n-1}$ then the nilpotence class of $G$ is at most 2 or $G$ has maximal class.