  We show that for the family of complex reflection groups $G=G(m,p,2)$
appearing in the Shephard--Todd classification, the endomorphism ring of the
reduced hyperplane arrangement $A(G)$ is a non-commutative resolution for the
coordinate ring of the discriminant $\Delta$ of $G$. This furthers the work of
Buchweitz, Faber and Ingalls who showed that this result holds for any true
reflection group. In particular, we construct a matrix factorization for
$\Delta$ from $A(G)$ and decompose it using data from the irreducible
representations of $G$. For $G(m,p,2)$ we give a full decomposition of this
matrix factorization, including for each irreducible representation a
corresponding a maximal Cohen--Macaulay module. The decomposition concludes
that the endomorphism ring of the reduced hyperplane arrangement $A(G)$ will be
a non-commutative resolution.
