Work

The character table of a subgroup $2^{16}{:}Sp_{8}(2)$ of $E_6(2)$

Year: 2024

Type: article

Abstract: The symplectic group $ Sp_{8}(2) $ has a unique absolutely irreducible module $ 2^{16} $ of dimension 16 over $GF(2)$. Hence a split extension group $\overline{G}$ of the form $2^{16}{:}Sp_{8}(2)$ exists. The structure of the group $\overline{G}$ makes it most suitable for a standard application of the Fischer-Clifford matrices technique to compute its ordinary character table. Since this is a very large group it will not be possible to compute its character table in GAP or MAGMA with an average computer device. An existing GAP routine which computes candidates for the Fischer-Clifford matrices of an extension group, such as $\overline{G}$, also fails. This makes $\overline{G}$ a very interesting group for an application of the Fischer-Clifford matrices technique. In this paper, the authors use mostly brute force and some GAP subroutines to construct the Fischer-Clifford matrices and ordinary character table of $\overline{G}$.

Source: Proyecciones (Antofagasta)

DOI: 10.22199/issn.0717-6279-6393

Authors: Abraham Prins, David Mwanzia Musyoka, Lydia Nyambura Njuguna, Lucy Chikamai

Institutions: Nelson Mandela University, Kenyatta University, Kibabii University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Research Foundation

Award: G974385828