The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24-Reference-Cited by-同舟云学术

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

Published:2010-09 Issue:03 Volume:17 Page:389-414
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Ali Faryad¹,Moori Jamshid²

Affiliation:

1. Department of Mathematics, Faculty of Sciences, Al-Imam Mohammed Bin Saud Islamic University, P.O. Box 90950, Riyadh 11653, Saudi Arabia

2. School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X 01, Scottsville, Pietermaritzburg 3209, South Africa

Abstract

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386710000386

Reference13 articles.

1. The Fischer-Clifford matrices of a maximal subgroup of 𝐹𝑖′₂₄

2. The multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups

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