On a Maximal Subgroup 2^6:(3^. S6) of M24

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics, The Copperbelt University, Kitwe Campus, Zambia

2 Department of Mathematical and Computer Sciences, University of Limpopo, Polokwane, South Africa

Abstract

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.

Keywords

References

[1] F. Ali, Fischer-Clifford Theory for Split and Non-Split Group Extensions, PhD Thesis, University of Kwazulu-Natal, Pietermaritzburg, 2001.
[2] A. B. M. Basheer and J. Moori, Fischer matrices of Dempwolff group 25.GL(5,2), Int. J. Group Theory 1 (4) (2012) 43–63.
[3] A. B. M. Basheer and J. Moori, On a group of the form 37.Sp(6,2), Int. J. Group Theory 5 (2) (2016) 41–59.
[4] A. B. M. Basheer and T. T. Seretlo, On a group of the form 214:Sp(6,2), Quaest. Math 39 (1) (2016) 45–57.
[5] D. S. Chikopela, Clifford-Fischer Matrices and Character Tables of Certain Group Extensions Associated with M22 :2, M24 and HS:2, MSc, North-West University, Mafikeng, 2016.
[6] C. Chileshe and J. Moori, On a maximal parabolic subgroup of O+8 (2), Bull. Iranian Math. Soc. 44 (1) (2018) 159–181.
[7] C. Chileshe, Irreducible Characters of Sylow p − Subgroups Associated with some Classical Linear Groups, PhD Thesis, North West University, Mafikeng Campus, 2016.
[8] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
[9] B. Fischer, Clifford-Matrices, in Representation Theory of Finite Groups and Finite Dimensional Algebras, G. O. Michler and C. M. Ringel (eds), Progr. Math. 95 (1–16), Birkhauser, Basel, 1991.
[10] The GAP Group, GAP − Groups, Algorithms, and Programming, Version 4.10.2, 2019.
[11] I. M. Isaacs, Character Theory of Finite Groups, Academic Press New York, San Francisco, London, 1976.
[12] R. J. List, On the characters of 2n−ϵ :Sn , Arch. Math. (Basel) 15 (1988) 118–124.
[13] J. Moori, On certain groups associated with the smallest Fischer group, J. London Math. Soc. (2) 23 (1) (1981) 61–67.
[14] Z. E. Mpono, Fischer Clifford Theory and Character Tables of Group Extensions, PhD Thesis, University of Kwazulu-Natal, Pietermaritzburg, 1998.
[15] T. T. Seretlo and J. Moori, On an inertia factor group of 2 8 :O+8 (2), Ital. J. Pure Appl. Math. 33 (2014) 241–254.
[16] T. T. Seretlo, Fischer Clifford Theory and Character Tables of Certain Groups Associated with Simple Groups O+10 (2), HS and Ly, PhD Thesis, University of Kwazulu-Natal, Pietermaritzburg, 2011.
[17] N. S. Whitley, Fischer Matrices and Character Tables of Group Extensions, MSc, University of Kwazulu-Natal, Pietermaritzburg, 1994.
[18] R. A. Wilson, R. P. Walsh, J. Tripp, I. Suleiman, S. Rogers, R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray and R. Abbot, Atlas of Finite Group Representation, http://brauer.maths.qmul.ac.uk/Atlas/v3/, 2006.
Mathematics Interdisciplinary Research
Volume 7, Issue 3
September 2022
Pages 197-216

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