Character degrees of some $p$-groups

Abstract: We restrict the possibilities for the character degrees of $p$-groups $G$ satisfying $|G:G&#39;| = p<sup>2$. E.g. if $G$ is of maximal class and has an irreducible character of degree $&gt; p$, then it has such a character of degree at most $p<sup>{\frac{p+1}{2}}$.