The $Z_k \times D_{k'}$ Brane Box Model

An example of a non-Abelian Brane Box Model, namely one corresponding to a $Z_k \times D_{k'}$ orbifold singularity of $\C^3$, is constructed. Its self-consistency and hence equivalence to geometrical methods are subsequently shown. It is demonstrated how a group-theoretic twist of the non-Abelian group circumvents the problem of inconsistency that arise from na\"{\i}ve attempts at the construction.