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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The computations were carried out using the computer algebra systems MAGMA [9] and GAP [29].
📌 3 Key Takeaways
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Objective & Hypothesis:The sporadic simple group F i22 is generated by a conjugacy class D of 3510 Fischer’s 3-transpositions.
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Key Findings & Data:In F i22 there are 14 classes of maximal subgroups up to conjugacy as listed in the ATLAS [10] and Wilson [31].
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Conclusion & Impact:The computations were carried out using the computer algebra systems MAGMA [9] and GAP [29].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fischer-Clifford matrix · extension · Fischer group F i22
Abstract
The sporadic simple group F i22 is generated by a conjugacy class D of 3510 Fischer’s 3-transpositions. In F i22 there are 14 classes of maximal subgroups up to conjugacy as listed in the ATLAS [10] and Wilson [31]. The group E = 26 :Sp6(2) is maximal subgroup of F i22 of index 694980. In the present article we compute the Fischer-Clifford matrices and hence character table of a subgroup of the smallest Fischer group F i22 of the form 26 :S8 which sits maximally in E. The computations were carried out using the computer algebra systems MAGMA [9] and GAP [29].
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Cite This Article
Ali, F., Moori, J. (2014). The Fischer-Clifford matrices and character table of the split extension 2 6 :S8. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 2. https://ajindex.com/articles/1403407