[GAP Forum] Fusion of Conjugacy Classes

[Thomas Breuer]

Dear Forum,

Marek Mitros wrote:

> Can anyone comment on following problem with fusion of 6th maximal subgroup
> of Baby Monster group ?
> 
> gap> bt:=CharacterTable("B");
> CharacterTable( "B" )
> gap> b6t:=CharacterTable("BM6");
> CharacterTable( "(2^2xF4(2)):2" )
> gap> fu:=FusionConjugacyClasses(b6t,bt);
> fail
> 
> Fusion for remaining 29 maximal subgroups of B can be obtained. E.g.
> b7t:=CharacterTable("BM6"); FusionConjugacyClasses(b7t,bt);
> 
> works fine. I am using GAP 4.7.4 on Windows 7.

The class fusions for the other 29 maximal subgroups
are stored on the character tables, but this one is not.
The reason why one fusion is missing is simply that I do not know it;
the necessary conditions leave several nonequivalent possibilities.

Up to now, all questions which I had about this maximal subgroup of
the Baby Monster have been be answered by checking the possible fusions.
Thus determining the fusion had low priority.

All the best,
Thomas