The Projective Character Tables of a Solvable Group 26 : (6 × 2)

Abstract

The Chevalley–Dickson simple group G2(4) of Lie type G2 over the Galois field GF(4) and of order 251596800 =212.33.52.7.13 has a class of maximal subgroups of the form 24+6 : (A5 × 3), where 24+6 is a special 2-group with center Z(24+6) = 24 . Since 24 is normal in 24+6 : (A5 × 3), the group 24+6 : (A5 × 3) can be constructed as a nonsplit extension group of the form G = 24 · (26 : (A5 × 3)). Two inertia factor groups, H1 = 26 : (A5 × 3) and H2 = 26 : (6 × 2), are obtained if G acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. +ese tables become very useful if one wants to construct the ordinary character table of G by means of Fischer–Clifford theory. +e method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size.