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On the inertia groups of the maximal subgroup 2<sup>7</sup>:<i>Sp<sub>6</sub></i>(2) in <i>Aut</i>(<i>Fi<sub>22</sub></i>)
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).
Keywords: Coset analysis, Fischer-Clifford matrices, permutation character.
