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One of the 26 finite Simple Groups. The most complicated is the Monster Group. A summary, as given by Conway et al. (1985), is given below.
Symbol | Name | Order | ![]() |
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Mathieu |
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1 | 1 |
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Mathieu |
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2 | 2 |
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Mathieu |
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12 | 2 |
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Mathieu |
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1 | 1 |
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Mathieu |
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1 | 1 |
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Janko |
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2 | 2 |
Suz | Suzuki |
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6 | 2 |
HS | Higman-Sims |
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2 | 2 |
McL | McLaughlin |
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3 | 2 |
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Conway |
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1 | 1 |
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Conway |
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1 | 1 |
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Conway |
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2 | 1 |
He | Held |
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1 | 2 |
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Fischer |
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6 | 2 |
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Fischer |
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1 | 1 |
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Fischer |
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3 | 2 |
HN | Harada-Norton |
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1 | 2 |
Th | Thompson |
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1 | 1 |
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Baby Monster |
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2 | 1 |
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Monster |
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1 | 1 |
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Janko |
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1 | 1 |
O'N | O'Nan |
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3 | 2 |
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Janko |
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3 | 2 |
Ly | Lyons |
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1 | 1 |
Ru | Rudvalis |
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2 | 1 |
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Janko |
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1 | 1 |
See also Baby Monster Group, Conway Groups, Fischer Groups, Harada-Norton Group, Held Group, Higman-Sims Group, Janko Groups, Lyons Group, Mathieu Groups, McLaughlin Group, Monster Group, O'Nan Group, Rudvalis Group, Suzuki Group, Thompson Group
References
Aschbacher, M. Sporadic Groups. New York: Cambridge University Press, 1994.
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.
Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups.
Oxford, England: Clarendon Press, p. viii, 1985.
Math. Intell. Cover of volume 2, 1980.
Wilson, R. A. ``ATLAS of Finite Group Representation.''
http://for.mat.bham.ac.uk/atlas/html/contents.html#spo.
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© 1996-9 Eric W. Weisstein