On a maximal subgroup of the Symplectic group Sp(4,4)

Document Type : Original Article

Author

School of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P Bag X1106, Sovenga 0727, South Africa

Abstract

This paper is dealing with a split extension group of the form 26 :(3× A5), which is the largest maximal subgroup of the Symplectic group Sp(4, 4). We refer to this extension by G. We firstly determine the conjugacy classes of G using the coset analysis technique. The structures of inertia factor groups were determined. We then compute the Fischer matrices of G and apply the Clifford-Fischer theory to calculate the ordinary character table of this group. The Fischer matrices of G are all integer valued, with sizes ranging from 1 to 4. The full character table of G is 26×26 complex valued matrix and is given at the end of this paper.

Keywords

Main Subjects

References

[1] Maxima, a computer algebra system. version 5.18.1. http://maxima.sourceforge.net. Accessed: 2009.
[2] The GAP Group, gap – groups, algorithms, and programming, version 4.4.10. http://www.gap-system.org. Accessed: 2007.
[3] A. B. M. Basheer, Clifford-Fischer theory applied to certain groups associated with symplectic, unitary and Thompson groups, PhD thesis, University of KwaZulu-Natal, Pietermaitzburg, 2012.
[4] A. B. M. Basheer, F. Ali, and M. L. Alotaibi, On a maximal subgroup of the Conway simple group Co3, Ital. J. Pure Appl. Math., (2020), pp. 357–372.
[5] A. B. M. Basheer and J. Moori, Fischer matrices of Dempwolff group 2 5.GL(5, 2), Int. J. Group Theory, 1 (2012), pp. 43–63.
[6] A. B. M. Basheer and J. Moori, On the non-split extension group 2 6·Sp(6, 2), Bull. Iranian Math. Soc., 39 (2013), pp. 1189–1212.
[7] A. B. M. Basheer and J. Moori, On a maximal subgroup of the Thompson simple group, Math. Commun., 20 (2015), pp. 201–218.
[8] A. B. M. Basheer and J. Moori, On the non-split extension 2 2n·Sp(2n, 2), Bull. Iranian Math. Soc., 41 (2015), pp. 499–518.
[9] A. B. M. Basheer and J. Moori, A survey on Clifford-Fischer theory, in Groups St Andrews 2013, vol. 422 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 2015, pp. 160–172.
[10] A. B. M. Basheer and T. T. Seretlo, On a group of the form 3 7 : Sp(6, 2), Int. J. Group Theory, 5 (2016), pp. 41–59.
[11] A. B. M. Basheer and J. Moori, Clifford-Fischer theory applied to a group of the form 2 1+6 − : ((31+2 : 8) : 2), Bull. Iranian Math. Soc., 43 (2017), pp. 41–52.
[12] A. B. M. Basheer and J. Moori, On a group of the form 2 10 : (U5(2) : 2), Ital. J. Pure Appl. Math., (2017), pp. 645–658.
[13] A. B. M. Basheer and J. Moori, On two groups of the form 2 8 :A9, Afr. Mat., 28 (2017), pp. 1011–1032.
[14] A. B. M. Basheer and J. Moori, On a maximal subgroup of the affine general linear group of GL(6, 2), Adv. Group Theory Appl., 11 (2021), pp. 1–30.
[15] W. Bosma and J. Cannon, Handbook of magma functions, 1994.
[16] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.
[17] J. Moori, On the groups G+ and G of the form 2 10:M22 and 2 10:M22, PhD thesis, University of Brimingham, 1975.
[18] J. Moori, On certain groups associated with the smallest Fischer group, J. London Math. Soc. (2), 23 (1981), pp. 61–67.
[19] T. T. Seretlo, Fischer-Clifford matrices and character tables of certain groups associated with simple groups O + 10(2), HS and Ly, PhD thesis, University of KwaZulu-Natal, Pietermaritzburg, 2012.
[20] N. S. Whitley, Fischer matrices and character tables of group extensions, Master’s thesis, 1994.
[21] R. Wilson, P. Walsh, J. Tripp, I. Suleiman, S. Rogers, R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray, et al., Atlas of finite group representations. http://brauer.maths.qmul.ac.uk/ Atlas/v3/, 1999.
AUT Journal of Mathematics and Computing
Volume 4, Issue 1
2023
Pages 17-26

Files

Share

How to cite

Statistics