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.
Basheer, A. (2023). On a maximal subgroup of the Symplectic group $Sp(4,4)$. AUT Journal of Mathematics and Computing, 4(1), 17-26. doi: 10.22060/ajmc.2022.21693.1099
MLA
Ayoub Basheer Mohammed Basheer. "On a maximal subgroup of the Symplectic group $Sp(4,4)$". AUT Journal of Mathematics and Computing, 4, 1, 2023, 17-26. doi: 10.22060/ajmc.2022.21693.1099
HARVARD
Basheer, A. (2023). 'On a maximal subgroup of the Symplectic group $Sp(4,4)$', AUT Journal of Mathematics and Computing, 4(1), pp. 17-26. doi: 10.22060/ajmc.2022.21693.1099
VANCOUVER
Basheer, A. On a maximal subgroup of the Symplectic group $Sp(4,4)$. AUT Journal of Mathematics and Computing, 2023; 4(1): 17-26. doi: 10.22060/ajmc.2022.21693.1099
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