Degree of irreducible projective representation divides index of cyclic normal subgroup

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Statement

Suppose G is a finite group, H is a Cyclic normal subgroup (?) of G, and K is an algebraically closed field whose characteristic does not divide the order of G. Suppose that \varphi is an irreducible projective representation of G over K.

Then, the degree of \varphi divides the index of H in G.

This is a numerical constraint on the Degrees of irreducible projective representations (?).

Related facts

Corollaries

Ordinary representations

Facts used

  1. Degree of irreducible projective representation divides index of abelian normal subgroup to which its cohomology class restricts trivially
  2. Cyclic implies Schur-trivial

Proof

The proof follows directly from Facts (1) and (2).