  We consider the action of $p$-toral subgroups of $U(n)$ on the unitary
partition complex $\mathcal L_n$. We show that if $H\subseteq U(n)$ is
$p$-toral and has noncontractible fixed points on $\mathcal L_n$, then the
image of $H$ in the projective unitary group $U(n)/S^{1}$ is an elementary
abelian $p$-group.
