  In this paper we expand on previous results, studying the extent to which one
can detect fusion in certain finite groups $\Gamma$, from information about the
universal deformation rings of absolutely irreducible
$\mathbb{F}_p\Gamma$-modules. We consider groups which are extensions of finite
irreducible subgroups of $Gl_2({\mathbb{C}})$ by elementary abelian $p$-groups
of rank $2$.
