ON A GROUP EXTENSION INVOLVING THE SPORADIC JANKO GROUP \(J_{2}\)

Abstract

Using the electronic Atlas of Wilson [21], the group J_2 has an absolutely irreducible module of dimension 6 over F_4. Therefor a split extension group of the form 4^6:J_2:= \bar{G} exists. In this paper we study this group, where we determine its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. We determined the inertia factor groups of \bar{G} by analysing the maximal subgroups of J_2 and maximal of the maximal subgroups of J_2 together with other various information. It turns out that the character table of \bar{G} is a 53 x 53 real valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 8.

Keywords

• group extensions, janko sporadic simple group, inertia groups, fischer matrices, character table