Hi,
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.
Is there some technique which reduce the necessary calculation in GAP?
I also want to compute the pre-image subgroup of
WreathProduct(Normalizer(SymmetricGroup(5),SylowSubgroup(SymmetricGroup(5),5)),SymmetricGroup(2));
via $h$ in $g$ which has cardinarity 1600.
Sincerely,
Shunsuke
f:=FreeGroup(10);
g:=f/[f.1^2*f.10^(-1),f.2^2*f.10^(-1),f.3^2*f.10^(-1),f.4^2*f.10^(-1),f.5^2*f.10
^(-1),f.6^2*f.10^(-1),f.7^2*f.10^(-1),f.8^2*f.10^(-1),f.9^2*f.10^(-1),(f.1*f.2)^
3*f.10^(-1),(f.2*f.3)^3*f.10^(-1),(f.3*f.4)^3*f.10^(-1),(f.4*f.5)^3*f.10^(-1),(f
.5*f.6)^3*f.10^(-1),(f.6*f.7)^3*f.10^(-1),(f.7*f.8)^3*f.10^(-1),(f.8*f.9)^3*f.10
^(-1),(f.1*f.3)^2*f.10^(-1),(f.1*f.4)^2*f.10^(-1),(f.1*f.5)^2*f.10^(-1),(f.1*f.6
)^2*f.10^(-1),(f.1*f.7)^2*f.10^(-1),(f.1*f.8)^2*f.10^(-1),(f.1*f.9)^2*f.10^(-1),
(f.2*f.4)^2*f.10^(-1),(f.2*f.5)^2*f.10^(-1),(f.2*f.6)^2*f.10^(-1),(f.2*f.7)^2*f.
10^(-1),(f.2*f.8)^2*f.10^(-1),(f.2*f.9)^2*f.10^(-1),(f.3*f.5)^2*f.10^(-1),(f.3*f
.6)^2*f.10^(-1),(f.3*f.7)^2*f.10^(-1),(f.3*f.8)^2*f.10^(-1),(f.3*f.9)^2*f.10^(-1
),(f.4*f.6)^2*f.10^(-1),(f.4*f.7)^2*f.10^(-1),(f.4*f.8)^2*f.10^(-1),(f.4*f.9)^2*
f.10^(-1),(f.5*f.7)^2*f.10^(-1),(f.5*f.8)^2*f.10^(-1),(f.5*f.9)^2*f.10^(-1),(f.6
*f.8)^2*f.10^(-1),(f.6*f.9)^2*f.10^(-1),(f.7*f.9)^2*f.10^(-1),f.10*f.10];
imgs:=[(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,10),()];
h:=GroupHomomorphismByImages(g,SymmetricGroup(10),GeneratorsOfGroup(g),imgs);
W:=WreathProduct(SymmetricGroup(5),SymmetricGroup(2));
Pr:=PreImage(h,W);
gap> Size(Pr);
#I Coset table calculation failed -- trying with bigger table limit
#I Coset table calculation failed -- trying with bigger table limit
#I Coset table calculation failed -- trying with bigger table limit
57600
gap> c:=CharacterTable(Pr);
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