  Let $k$ be an algebraically closed field of prime characteristic $p$ and $P$
a finite $p$-group. We compute the Scott $kG$-module with vertex $P$ when
$\mathcal{F}$ is a constrained fusion system on $P$ and $G$ is Park's group for
$\mathcal{F}$. In the case $\mathcal{F}$ is a fusion system of the quadratic
group $Qd(p)=(\mathbb{Z}/p \times \mathbb{Z}/p)\rtimes {\mathrm{SL}}(2,p)$ on a
Sylow $p$-subgroup $P$ of $Qd(p)$ and $G$ is Park's group for $\mathcal{F}$, we
prove that the Scott $kG$-module with vertex $P$ is Brauer indecomposable.
