Projective representations of abelian groups

Let co be a factor system for the locally compact abelian group G. Then we show that the finite-dimensional unitary irreducible projective representations of G, having factor system co, possess a common dimension d(wo). Using a characterisation of d (o) as the index in G of a maximal subgroup on which ao is symmetric we derive a formula for d(wo) in the case that G is discrete and finitely generated.