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

Authors :
Ali, Faryad
Moori, Jamshid
Jiping Zhang
Source :
Algebra Colloquium. Sep2010, Vol. 17 Issue 3, p389-414. 26p. 10 Charts.
Publication Year :
2010

Abstract

The Fischer group $Fi_{24}={\rm Aut} (Fi_{24}^{\prime})$ 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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10053867
Volume :
17
Issue :
3
Database :
Academic Search Index
Journal :
Algebra Colloquium
Publication Type :
Academic Journal
Accession number :
51993886
Full Text :
https://doi.org/10.1142/S1005386710000386