Clifford-Fischer theory on an affine subgroup of GO(5,3)

Abstract

In this paper we apply the Clifford-Fischer Theory to an affine subgroup G―=33:GO(3,3) of the general orthogonal group GO(5,3) to compute Fischer matrices of G― to ultimately construct a character table of G―. According to the ATLAS we have that GO(5,3) is isomorphic to 2×(O(5,3):2) where O(5,3) is the simple orthogonal group isomorphic to the simple symplectic group S4(3). The affine subgroup G― sits maximally in O(5,3):2. The affine subgroup of the full symplectic group Sp(4,3) is 33:S4. The subgroup G― sits maximally in Sp(4,3) containing the affine subgroup of Sp(4,3).

The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗