  Let p be a prime number. Let G be a finite p-group and $\chi \in Irr(G)$.
Denote by $\bar{\chi} \in Irr(G)$ the complex conjugate of $\chi$. Assume that
$\chi(1)=p^n$. We show that the number of distinct irreducible constituents of
the product $\chi\bar{\chi}$ is at least $2n(p-1)+1$.
