^{1}
School of Mathematical Sciences, North-West University (Mafikeng)
^{2}
North-West University
Abstract
In this paper we give some general results on the non-split extension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq 2.$ We then focus on the group $overline{G}_{4} = 2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as a permutation group acting on 512 points. The conjugacy classes are determined using the coset analysis technique. Then we determine the inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}_{4}$ by means of Clifford-Fischer Theory. There are two inertia factor groups namely $H_{1} = Sp(8,2)$ and $H_{2} = 2^{7}{:}Sp(6,2),$ the Schur multiplier and hence the character table of the corresponding covering group of $H_{2}$ were calculated. Using the information on conjugacy classes, Fischer matrices and ordinary and projective tables of $H_{2},$ we concluded that we only need to use the ordinary character table of $H_{2}$ to construct the character table of $overline{G}_{4}.$ The Fischer matrices of $overline{G}_{4}$ are all listed in this paper. The character table of $overline{G}_{4}$ is a $195 times 195$ complex valued matrix, it has been supplied in the PhD Thesis of the first author, which could be accessed online.
Basheer, A., Moori, J. (2015). On the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$. Bulletin of the Iranian Mathematical Society, 41(2), 499-518.
MLA
A. B. M. Basheer; J. Moori. "On the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$". Bulletin of the Iranian Mathematical Society, 41, 2, 2015, 499-518.
HARVARD
Basheer, A., Moori, J. (2015). 'On the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$', Bulletin of the Iranian Mathematical Society, 41(2), pp. 499-518.
VANCOUVER
Basheer, A., Moori, J. On the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$. Bulletin of the Iranian Mathematical Society, 2015; 41(2): 499-518.