Dear Forum, Dear Shunsuke Tsuchioka,
> I want to get a character table of a group of order 57600.
>
> Let $g$ be a Schur Cover of the symmetric group of degree 10
> and $h: g \twoheadrightarrow S_{10}$ be a natural surjection.
> A wreath product $W:=S_{5}\wr S_{2}$ is naturally identified
> with a subgroup of $S_{10}$. I want to get the character table
> of the preimage subgroup $h^{-1}(W)$ of $g$.
> As shown below, it seems intractable by a naive approach.
You're almost there. The problem is that more involved calculations tend to be
inefficient for finitely presented groups. (This is a fundamental issue with
such groups, not just a lack of methods.)
Thus the best way to proceed is to convert to a permutation group, via
converting Pr first to a finitely presented group on its own:
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: hul...@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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