The Fischer-Cliford Matrices and Character Table of the Group 𝟐𝟔:𝑺𝟕

Rauhi Ibrahim Elkhatib

Abstract


The split extension alternating group  of order 322560 with index 28431 is a maximal subgroup of the orthogonal group  of order . This Group has four inertia factor groups namely,  ,  ,      and  of indices 1, 7, 21 and 35 respectively in  . The aim of this paper is to construct the Fischer-Clifford matrices of , which together with the associated partial character tables of the inertia groups, are used to compute the full charter table of . There are 15 Ficsher-Clifford matrices with sizes between  and .


Keywords


linear groups, group extensions, character table, Clifford theory, inertia groups, Fischer-Clifford matrix.

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References


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