[GAP Forum] Projective representations

[D N]

Dear GAP Forum,
   
  Let us work over an algebraically closed field k of characteristic 0.
Let H be a finite group and let f : H x H --> k* be a 2-cocycle.
Here k* is the abelian group of non-zero elements of k considered as a
trivial module over H.
   
  Let V be a projective representation of H with 2-cocycle f.
Then the dual vector space V* is a projective representation of H
with 2-cocycle 1/f.
   
  The tensor product V \otimes V* is a representation of H.
Is it true that the decomposition of this representation (into 
irreducible representations of H) contains atleast one copy of the
trivial representation of H? If this is not true, then is there a way to use GAP to
  generate counter-examples?
   
  Any help towards answering this question is greatly appreciated.
   
  Thanks,
D. Naidu
       
 
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