  In this paper, we classify conjugacy classes of centralizers of irreducible
subgroups in $PSL(n,\mathbb{C})$ using alternate modules a.k.a. finite abelian
groups with an alternate bilinear form. When $n$ is squarefree, we prove that
these conjugacy classes are classified by their isomorphism classes. More
generally, we define a finite graph related to this classification whose
combinatorial properties are expected to help us describe the stratification of
the singular (orbifold) locus in some character varieties.
