Open AccessOn a maximal subgroup of the orthogonal group O⁺₈(3)
Author(s) -
David Mwanzia Musyoka,
Lydia N. Njuguna,
Abraham Love Prins,
Lucy Chikamai
Publication year - 2022
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4778
Subject(s) - character table , mathematics , conjugacy class , combinatorics , group (periodic table) , character (mathematics) , orthogonal group , normal subgroup , maximal subgroup , pure mathematics , discrete mathematics , geometry , chemistry , organic chemistry
The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups of the form 36:L4(3). These groups are all isomorphic to each other and each group has order 4421589120 with index 1120 in 0 (3). In this paper, we will compute the ordinary carácter table of one of these classes of maximal subgroups using the technique of Fischer-Clifford matrices. This technique is very efficient to compute the ordinary character table of an extension group Ḡ = N.G and especially where the normal subgroup N of Ḡ is an elementary abelian p-group. The said technique reduces the computation of the ordinary character table of Ḡ to find a handful of so-called Fischer-Clifford matrices of Ḡ and the ordinary or projective character tables of the inertia factor groups of the action of Ḡ on N.