Search

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G:X) to be the minimum number of elements of X generating G. Moori investigated rank(Fi22:X), where X is a conjugacy class of involutions in the Fischer group Fi22. In the present article, we completely determine the ranks of the Fischer group Fi22 by computing rank(Fi22:X), where X is any conjugacy class of Fi22.Keywords: Fischer group Fi22, rank, generator, sporadic groupQuaestiones Mathematicae 37(2014), 591-600

http://www.hjms.hacettepe.edu.tr/Search?q=The%20Fischer-Clifford%20matrices%20and%20character%20table%20of%20the%20split%20extension%2026:S8

The sporadic simple group F i22 is generated by a conjugacy class D of3510 Fischer’s 3-transpositions. In F i22 there are 14 classes of maximalsubgroups 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 index694980. In the present article we compute the Fischer-Clifford matricesand hence character table of a subgroup of the smallest Fischer groupF i22 of the form 26:S8 which sits maximally in E. The computationswere carried out using the computer algebra systems MAGMA [9] andGAP [29].&nbsp