On a two-fold cover 2.(2⁶˙G₂(2)) of a maximal subgroup of Rudvalis group Ru

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4574

Keywords:

Non-split extension, Projective character table, Factor set, Schur multiplier, Representation group, Inertia factor groups, Fischer matrices

Abstract

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G(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˙G(2)) exists for Ḡ1. Furthermore, Ḡ1 will have four sets IrrProj(Ḡ1i) 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. Ḡ1 of Ḡ1 which can be treated as a non-split extension of the form Ḡ = 2G2(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(Ḡ1; α2) of irreducible projective characters of Ḡ1 with factor set α2 such that α22= 1, can be obtained.

Author Biography

Abraham Love Prins, Nelson Mandela University.

Dept. of Mathematics and Applied Mathematics

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Published

2021-04-19 — Updated on 2021-07-26

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How to Cite

[1]
A. L. Prins, “On a two-fold cover 2.(2⁶˙G₂(2)) of a maximal subgroup of Rudvalis group Ru”, Proyecciones (Antofagasta, On line), vol. 40, no. 4, pp. 1011-1029, Jul. 2021.

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