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 $2^{6}{:}(3 \times A_{5}),$ which is the largest maximal subgroup of the Symplectic group $Sp(4,4).$ We refer to this extension by $\overline{G}.$ We firstly determine the conjugacy classes of $\overline{G}$ using the coset analysis technique. The structures of inertia factor groups were determined. We then compute the Fischer matrices of $\overline{G}$ and apply the Clifford-Fischer theory to calculate the ordinary character table of this group. The Fischer matrices of $\overline{G}$ are all integer valued, with sizes ranging from 1 to 4. The full character table of $\overline{G}$ is $26 \times 26$ complex valued matrix and is given at the end of this paper.

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References

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AUT Journal of Mathematics and Computing
Volume 4, Issue 1
2023
Pages 17-25

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