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Ayoub Basheer
a:1:{s:5:"en_US";s:22:"University of Limpopo ";}
Mathematics

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On A Group Involving The Automorphism of The Janko Group J2 Ayoub Basheer
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 2 (JULY 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.2.1371.197-216

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.
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