On the degrees of projective representations

Abstract

All representations and characters studied in this paper are taken over the complex numbers, and all groups considered are finite. For basic definitions concerning projective representations see [1].If G is a group and or is a cocycle of G we denote by Proj(G, α) = {ξ1, …, ξt} the set of irreducible projective characters of G with cocycle α, where of course t is the number of α-regular conjugacy classes of G; ξ1, (1) is called the degree of ξ1. Also as normal, M(G) will denote the Schur multiplier of G, [α] the cohomology classof α, and [1] the cohomology class of the trivial cocycle of G.