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

Document Type : Original Article


Department of Mathematics University of Limpopo


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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