On a Group of the Form 2¹¹:M24.

The Conway group Co1 is one of the 26 sporadic simple groups. It is the largest of the three Conway groups with order 4157776806543360000 = 221.39.54.7².11.13.23 and has 22 conjugacy classes of maximal subgroups. In this paper, we discuss a group of the form G = N : G, where N = 211 and G = M24. This group G = N : G = 211 : M24 is a split extension of an elementary abelian group N = 211 by a Mathieu group G = M24. Using the computed Fischer matrices for each class representative g of G and ordinary character tables of the inertia factor groups of G, we obtain the full character table of G. The complete fusion of G into its mother group Co1 is also determined using the permutation character of Co1. [ABSTRACT FROM AUTHOR]

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