[GAP Forum] Computation of Character Table

[Shunsuke Tsuchioka]

Dear Alexander Hulpke,

Although the command "Q:=FactorCosetAction(P,u);" takes some time,
your method works fine and I could get the character table of "Pr".
Thank you very much for answering.
Your answer is both educational and instructive.

Best,
Shunsuke

P.S.
I could also get the character table of
PreImage(h,WreathProduct(Normalizer(SymmetricGroup(5),SylowSubgroup(SymmetricGroup(5),5)),SymmetricGroup(2)));
by your method. Thank you again.


From: Alexander Hulpke <hulpke at math.colostate.edu>
Subject: Re: [GAP Forum] Computation of Character Table
Date: Mon, 23 May 2011 10:00:37 -0600

> hom:=IsomorphismFpGroup(Pr);
> iso:=IsomorphismPermGroup(Image(hom));
> P:=Image(iso);
> 
> At this point, the built-in permutation degree reduction in 4.4  does not seem to work well (the next release will be much better in this area). A naive approach is to act on the cosets of a random cyclic subgroup 
> 
> repeat u:=Subgroup(P,[Random(P)]);until 1=Size(Core(P,u));
> Q:=FactorCosetAction(P,u);
> R:=Image(Q);
> 
> Now
> CharacterTable(R);
> will work quickly.
> 
> Best,
> 
>    Alexander Hulpke
> 
> 
> 
> 
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
> http://www.math.colostate.edu/~hulpke
> 
> 
>