The character table of an involution centralizer in the Dempwolff group 2^5. <i>GL</i>₅(2)

Abstract

The Dempwolff group D = 2^5. GL₅(2) has an involution centralizer Ḡ  = C_D(2A) of the type 2^5. (2⁴:GL₄(2)) of index 31 and has order 10321920. In this paper, the Fischer-Clifford matrices of the non-split extension Ḡ are computed. Then the character table of Ḡ is constructed using these Fischer-Clifford matrices, the ordinary character table of 2⁴:GL₄(2) and the projective character tables of the inertia factor groups H₂ = 2⁴:(2³:GL₃(2)) and H₃ = GL₄(2) of Ḡ.

Keywords: Coset analysis, Fischer-Clifford matrices, permutation character, projective character, factor set