  Let $p$ be a prime number, let $H$ be a finite $p$-group, and let
$\mathbb{F}$ be a field of characteristic 0, considered as a trivial
$\mathbb{F} \mathrm{Out}(H)$-module. The main result of this paper gives the
dimension of the evaluation $S_{H,\mathbb{F}}(G)$ of the simple biset functor
$S_{H,\mathbb{F}}$ at an arbitrary finite group $G$. A closely related result
is proved in the last section: for each prime number $p$, a Green biset functor
$E_p$ is introduced, as a specific quotient of the Burnside functor, and it is
shown that the evaluation $E_p(G)$ is a free abelian group of rank equal to the
number of conjugacy classes of $p$-elementary subgroups of $G$.
