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

Authors : Faryad ALİ, Jamshid MOORİ

Pages : 153-171

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Publication Date : 2014-04-01

Article Type : Research Paper

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 :Sp6insert ignore into journalissuearticles values(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