On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru - Prins,Abraham Love (Universidad Católica del Norte, Departamento de Matemáticas, 2021)
Abstract The Schur multiplier M(Ḡ 1) ≅ 4 of the maximal subgroup Ḡ 1 = 26· G 2(2) of the Rudvalis sporadic simple group Ru is a cyclic group of order 4. Hence a full representative group R of the type R = 4.(26· G2(2)) exists for Ḡ 1. Furthermore, Ḡ 1 will have four sets IrrP roj(Ḡ 1, αi) of irreducible projective characters, where the associated factor sets α1, α2, α3 and α4, have orders of 1, 2, 4 and 4, respectively. In this paper, we will deal with a 2-fold cover 2. Ḡ 1 of Ḡ 1 which can be treated as a non-split extension of the form Ḡ = 27· G2(2). The ordinary character table of Ḡ will be computed using the technique of the so-called Fischer matrices. Routines written in the computer algebra system GAP will be presented to compute the conjugacy classes and Fischer matrices of Ḡ and as well as the sizes of the sets |IrrProj(Hi, αi)| associated with each inertia factor Hi. From the ordinary irreducible characters Irr(Ḡ) of Ḡ, the set IrrProj(Ḡ 1, α2) of irreducible projective characters of Ḡ 1 with factor set α2 such that α2 2 = 1, can be obtained.