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The following is just a follow up to my previous question. I have a finite group $H$ with 14 ordinary characters. The Schur multiplier $M(H) \cong 2^2$. Hence the group $H$ will have 3 sets of projective characters with non-trivial factor sets $\alpha_i^{-1}$ of order 2, $i =1,2,3$. How to I prove that the cardinality of each of the three sets of projective characters with factor sets $\alpha_i^{-1}$ cannot exceed $|Irr(H)| =14$ . Perhaps Geoff Robinson can be of help here again.
