On an imprimitive maximal subgroup of $SU_7(2)$

Musyoka, David Mwanzia; Prins, Abraham Love; Njuguna, Lydia Nyambura; Chikamai, Lucy

doi:10.22060/ajmc.2025.23932.1340

On an imprimitive maximal subgroup of $SU_7(2)$

Articles in Press

Document Type : Original Article

Authors

David Mwanzia Musyoka ¹

Abraham Love Prins ²

Lydia Nyambura Njuguna ³

Lucy Chikamai ⁴

¹ Department of Mathematics, Statistics and Actuarial Sciences Karatina University P. O. Box 1957-10101, Kenya

² Department of Computational Sciences, University of Fort Hare, Private Bag X1314, King William’s Town Road, Alice, 5700, South Africa

³ Department of Mathematics and Actuarial Science, Kenyatta University, PO Box 43844 - 00100, Nairobi, Kenya

⁴ Department of Mathematics and Actuarial Science, Kibabii University, PO Box 1699 - 50200, Bungoma, Kenya

10.22060/ajmc.2025.23932.1340

Abstract

The special unitary group $SU_{n}(q)$ has a maximal imprimitive subgroup with the structure $(q+1)^{n-1}{:}S_{n}$. The exceptions when the subgroup is not maximal are $SU_{3}(5)$, $SU_{4}(3)$ and $SU_{6}(2)$. In this paper, the ordinary character table of the maximal imprimitive subgroup $\overline{G}=3^{6}{:}S_{7}$ of $SU_{7}(2)=U_{7}(2)$ is computed by the Fischer-Clifford matrices technique. A combinatorial approach is adopted in the computation of the Fischer-Clifford matrices of $\overline{G}$.

Keywords

Character table

Fischer-Clifford matrix

Inertia factor

Coset analysis

Subjects