[GAP Forum] a GAPreadable table of the primitive finite subgroups of GL(n, C), for n small?
pjc at mcs.stand.ac.uk
pjc at mcs.stand.ac.uk
Thu Jun 26 12:41:23 BST 2014
It may be worse than you thought. I just got this from Martin Roeteller:
Dear Peter,

I was wrong in three ways: first of all it was not about the
classification of crystallographic groups, it was about the
finite subgroups of SU(n). And the dimension was not as
large as n=20, it was as small as n=3 (!!). And the
original classification was not due to Kneser, as I
thought, but was due to Blichfeldt.

The paper is Ludl, "Comments on the classification of the
finite subgroups of SU(3)", J Phys A Math Theory 44:255204,
2011. Also on the arxiv at http://arxiv.org/abs/1101.2308
and http://arxiv.org/abs/1310.3746. Apparently he found
missing subgroups, the smallest one being a split extension
of order 162.

Best,
Martin
> Dear all,
>
> has onyone compiled such a list, which would incorporate the
> classically known lists due to Blichfeldt for n=4 (with corrections),
> etc?
> (in particular the case n=4 is a bit questionable, as there were
> repeated publications of incomplete lists in this case).
>
> Thanks,
> Dima
>
> PS. an irreducible representation of a finite group is called
> primitive if it is not induced from a representation of a subgroup.
>
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