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Basheer A B M, Moori J, Prins A L, Seretlo T T. On a Group of the Form $2^{4+5}:GL(4,2)$. IJMSI 2024; 19 (2) :169-188
URL: http://ijmsi.ir/article-1-1950-en.html
URL: http://ijmsi.ir/article-1-1950-en.html
Abstract:
The affine general linear group 25:GL(5, 2) of GL(6, 2) has 6 conjugacy classes of maximal subgroups. The largest two maximal subgroups are of the forms 21+8:GL(4, 2) and 24+5:GL(4, 2). In this article we consider the group 24+5:GL(4, 2), which we denote by ${bar G}$. Firstly we determine its conjugacy classes using the coset analysis technique. The structures of the inertia factor groups are also determined. We then compute all the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of ${bar G}$. Using information on conjugacy classes, Fischer matrices and both ordinary and projective character tables of the inertia factor groups, we concluded that we need to use the ordinary character tables of all the inertia factor groups to construct the character table of ${bar G}$. The character table of ${bar G}$ is a 75×75 complex valued matrix and we supply it (in the format of Clifford-Fischer theory) at the end of this paper as Table 6.
Keywords: Group extensions, General linear group, Character table, Inertia factor groups, Fischer matrices.
Type of Study: Research paper |
Subject:
General
References
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