the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...

‎in our paper [a‎. ‎b‎. ‎m‎. ‎basheer and j‎. ‎moori‎, ‎on a group of the form $2^{10}{:}(u_{5}(2){:}2)$] we calculated the inertia factors‎, ‎fischer matrices and the ordinary character table of the split‎ ‎extension $ 2^{10}{:}(u_{5}(2){:}2)$ by means of clifford-fischer‎ ‎theory‎. ‎the second inertia factor group of $2^{10}{:}(u_{5}(2){:}2)$‎ ‎is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_{6}(2...

in this paper we first construct the non-split extension $overline{g}= 2^{6} {^{cdot}}sp(6,2)$ as a permutation group acting on 128 points. we then determine the conjugacy classes using the coset analysis technique, inertia factor groups and fischer matrices, which are required for the computations of the character table of $overline{g}$ by means of clifford-fischer theory. there are two inerti...

In this paper we give some general results on the non-splitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer...

The present paper deals with a maximal subgroup of the Thompson group, namely the group 2 + A9 := G. We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of G by means of Clifford-Fischer Theory. AMS subject classifications: 20C15, 20C40

‎in [u‎. ‎dempwolff‎, ‎on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$‎, ‎textit{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎, ‎textbf{48} (1972)‎, ‎359‎ - ‎364.] dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the‎ ‎elementary abelian group $2^{5}$ by the general linear group‎ ‎$gl(5,2)$)‎. ‎this group is the second l...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups the form 36:L4(3). These groups are all isomorphic to each other and order 4421589120 with index 1120 in (3). In this paper, we will compute ordinary carácter table one these using technique Fischer-Clifford matrices. This is very efficient character an extension Ḡ = N.G especially where normal subgroup N element...

Two useful theorems in Euclidean and Hermitean Clifford analysis are discussed: the Fischer decomposition and the Cauchy-Kovalevskaya extension.