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On the inertia groups of the maximal subgroup 2⁷:Sp₆(2) in Aut(Fi₂₂)

Published in: Quaestiones Mathematicae
Volume 38 , issue 1 , 2015 , pages: 83–102

DOI: 10.2989/16073606.2014.981709

Author(s): Richard Llewellyn Fray Department of Mathematics and Applied Mathematics, South Africa , Abraham Love Prins Department of Mathematics, Faculty of Military Science, South Africa

Keywords: Primary: 20C15 , Secondary: 20C40 , Primary: 20C15 , Secondary: 20C40

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Abstract

The group 2⁷:Sp₆(2) is a maximal subgroup of Aut(Fi₂₂) of index 694980. The group Aut(Fi₂₂) is the full automorphism group of the smallest Fischer simple group Fi₂₂. In this paper, we construct the character table of the inertia group 2⁷:(2⁵:S₆) of 2⁷:Sp₆(2) of index 63 through its Fischer-Clifford matrices. The split extension group 2⁷:(2⁵:S₆) sits maximally inside 2⁷:Sp₆(2).

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