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On a group of the form 2<sup>14</sup>:<i>Sp</i>(6,2)


Ayoub B.M. Basheer
Thekiso T. Seretlo

Abstract

The symplectic group Sp(6,2) has a 14-dimensional absolutely irreducible module over F2: Hence a split extension group of the form G = 214:Sp(6,2) does exist. In this paper we first determine the conjugacy classes of G using the coset analysis technique. The structures of inertia factor groups were determined. The inertia factor groups are Sp(6,2); (21+4 x 22):(S3 x S3); S3 x S6; PSL(2,8); (((22 x Q8):3):2):2, Sx A5; and 2 x Sx S3: We then determine the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of G: The Fischer matrices of G are all integer valued, with size ranging from 4 to 16. The full character table of G is a 186 x 186 complex valued matrix.

Keywords: Group extensions, Clifford theory, inertia groups, Fischer matrices, character table


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eISSN: 1727-933X
print ISSN: 1607-3606