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Submitted
February 3, 2023
Accepted
August 25, 2023
Published
July 31, 2023
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Abstract

The Janko sporadic simple group J2 has an automorphism group 2. Using the electronic Atlas of Wilson [22], the group J2:2 has an absolutely irreducible module of dimension 12 over F2. It follows that a split extension group of the form 2^12:(J2:2) := G exists. In this article we study this group, where we compute its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. The inertia factor groups of G will be determined by analysing the maximal subgroups of J2:2 and maximal of the maximal subgroups of J2:2 together with various other information. It turns out that the character table of G is a 64×64 real valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 6.

Keywords

Group extensions Janko sporadic simple group Inertia groups Fischer matrices ‎Character table.

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How to Cite
Basheer, A. (2023). On A Group Involving The Automorphism of The Janko Group J2. Journal of the Indonesian Mathematical Society, 29(2), 197–216. https://doi.org/10.22342/jims.29.2.1371.197-216
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