On a maximal subgroup of the orthogonal group O⁺₈ (3)


  • David Mwanzia Musyoka Kenyatta University.
  • Lydia Njuguna Kenyatta University.
  • Abraham Prins Nelson Mandela University.
  • Lucy Chikamai Kibabii University.




Coset analysis, Fischer-Clifford matrices, split extension, inertia factor, character table, fusion map, restriction of characters


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.

Author Biographies

David Mwanzia Musyoka, Kenyatta University.

Department of Mathematics and Actuarial Science,

Lydia Njuguna, Kenyatta University.

Department of Mathematics and Actuarial Science.

Abraham Prins, Nelson Mandela University.

Department of Mathematics and Applied Mathematics, Faculty of Science.

Lucy Chikamai, Kibabii University.

Department of Mathematics and Actuarial Science.


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How to Cite

D. M. . Musyoka, L. Njuguna, A. Prins, and L. . Chikamai, “On a maximal subgroup of the orthogonal group O⁺₈ (3)”, Proyecciones (Antofagasta, On line), vol. 41, no. 1, pp. 137-161, Jan. 2022.




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