The Fischer-Clifford matrices and character table of the split extension 2 6 :S8

Year 2014, Volume: 43 Issue: 2, 153 - 171, 01.04.2014

Faryad Ali Jamshid Moori

Abstract

The sporadic simple group F i22 is generated by a conjugacy class D of
3510 Fischer’s 3-transpositions. In F i22 there are 14 classes of maximal
subgroups up to conjugacy as listed in the ATLAS [10] and Wilson
[31]. The group E = 26
:Sp6(2) is maximal subgroup of F i22 of index
694980. In the present article we compute the Fischer-Clifford matrices
and hence character table of a subgroup of the smallest Fischer group
F i22 of the form 26
:S8 which sits maximally in E. The computations
were carried out using the computer algebra systems MAGMA [9] and
GAP [29]. 

Keywords

Fischer-Clifford matrix, extension, Fischer group F i22

References

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