[GAP Forum] Character group and semi-direct product

[D N]

Dear GAP Forum,
  
  Actually, I found (quite inefficient though) a way to do this.
  My apologies if the question and the follow-up is too trivial 
  to post on this forum.
  Let H be any Abelian group. The irreducible characters of H
  can be obtained by typing "Display(Irr(CharacterTable(H)));"
  Form diagonal matrices with rows of the above output. The
  group generated by these diagonal matrices is of course
  isomorphic to the character group  H^.  Putting the required
  action on H^ and forming the semidirect product is quite
  straight-forward.
  
  Thanks,
  DN
  
 
 
 
 D N <dn2447 at yahoo.com> wrote: Hello All,
 
 Let G be a finite group and H be a finite left G-module.
 Let H^  := Hom(H, C*) denote the character group of H.
 Then, H^ is a right G-module: (\rho \dot g)(h) := \rho(g  \dot h)
 for \rho \in H^, g \in G and h \in H.
 Let G' := H^ : G (semi-direct product of H^ and G).
 My question is: how to construct the group G' in GAP?
 
 Any help is greatly appreciated.
 
 Thanks,
 DN
 
 
  
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