On a group of the form 211:M24

Document Type : Original Article

Authors

Mathematics Department, School of Mathematics and Natural Sciences, Copperbelt University, Zambia

Abstract

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.

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References

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AUT Journal of Mathematics and Computing
Volume 5, Issue 2
2024
Pages 167-193

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