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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 1

On 2 nonsplit extension groups associated with HS and HS:2

Jamshid MOORI
Theskiso SERETLO
Pages
60–78
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The fusion of \overline{G}1 into \overline{G} is also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The group HS:2 is the full automorphism group of the Higman--Sims group HS.
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Key Findings & Data:The groups 24.S6 and 25.S6 are maximal subgroups of HS and HS:2, respectively.
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Conclusion & Impact:The fusion of \overline{G}1 into \overline{G} is also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Group extensions · Higman--Sims group · automorphism group

Abstract

The group HS:2 is the full automorphism group of the Higman--Sims group HS. The groups 24.S6 and 25.S6 are maximal subgroups of HS and HS:2, respectively. The group 24.S6 is of order 11520 and 25.S6 is of order 23040 and each of them is of index 3 850 in HS and HS:2, respectively. The aim of this paper is to first construct \overline{G} = 25.S6 as a group of the form 24.S6.2 (that is, \overline{G} = G1.2) and then compute the character tables of these 2 nonsplit extension groups by using the method of Fischer--Clifford theory. We will show that the projective character tables of the inertia factor groups are not required. The Fischer--Clifford matrices of \overline{G}1 and \overline{G} are computed. These matrices together with the partial character tables of the inertia factors are used to compute the full character tables of these 2 groups. The fusion of \overline{G}1 into \overline{G} is also given.

Özet

The group HS:2 is the full automorphism group of the Higman--Sims group HS. The groups 24.S6 and 25.S6 are maximal subgroups of HS and HS:2, respectively. The group 24.S6 is of order 11520 and 25.S6 is of order 23040 and each of them is of index 3 850 in HS and HS:2, respectively. The aim of this paper is to first construct \overline{G} = 25.S6 as a group of the form 24.S6.2 (that is, \overline{G} = G1.2) and then compute the character tables of these 2 nonsplit extension groups by using the method of Fischer--Clifford theory. We will show that the projective character tables of the inertia factor groups are not required. The Fischer--Clifford matrices of \overline{G}1 and \overline{G} are computed. These matrices together with the partial character tables of the inertia factors are used to compute the full character tables of these 2 groups. The fusion of \overline{G}1 into \overline{G} is also given.

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Cite This Article

MOORI, J., SERETLO, T. (2022). On 2 nonsplit extension groups associated with HS and HS:2. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 1, 60–78. https://ajindex.com/articles/608239

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