The Fischer-Clifford Matrices of a Maximal Subgroup of the Sporadic Simple Group of Held(Dedicated to Professor Jamshid Moori on the occasion of his 60th birthday)

• 来源期刊: 代数集刊（英文版）
• 关键词: Fischer-Clifford matrices non-split extension Held group
• 年，卷（期）: 2007,（1）
• 页码范围: 135-142
• 页数: 8页
• 语种: 英文

摘要

The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.3a.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the ATLAS. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He. In the present paper, we determine the Fischer Clifford matrices and hence compute the character table of the non-split extension 3.S7,which is a maximal subgroups of He of index 226560 using the technique of Fischer-Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system GAP.