%0 Journal Article
%T On a Maximal Subgroup 2^6:(3^. S6) of M24
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Chikopela, Dennis Siwila
%A Seretlo, Thekiso Trevor
%D 2022
%\ 09/01/2022
%V 7
%N 3
%P 197-216
%! On a Maximal Subgroup 2^6:(3^. S6) of M24
%K Mathieu group
%K Conjugacy classes
%K Irreducible characters
%K Fischer matrices
%K Fusions
%R 10.22052/mir.2022.243014.1300
%X The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters.
%U https://mir.kashanu.ac.ir/article_112777_4e1f0384dc40e18b6b1c38cce416a193.pdf