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

Ayoub B. M. Basheer     (School of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P. Bag X1106, Sovenga 0727, South Africa; Mathematics Program, Faculty of Education, Sohar, Oman;, South Africa)

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

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.1.003

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