Sporadic groups
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In mathematics, specifically group theory, the sporadic groups are a type of group which cannot be classified into any of the infinite families of simple groups.
There are 26 sporadic groups, the biggest being the Monster group (or Fischer-Griess monster), with a cardinality of approx. . The sporadic groups go as follows:
- 1. Mathieu groups M11, M12, M22, M23, M24
- 2. Janko groups J1, J2 or HJ, J3 or HJM, J4
- 3. Conway groups Co1, Co2, Co3
- 4. Fischer groups Fi22, Fi23, Fi24′ or F3+
- 5. Higman-Sims group HS
- 6. McLaughlin group McL
- 7. Held group He or F7+ or F7
- 8. Rudvalis group Ru
- 9. Suzuki group Suz or F3−
- 10. O'Nan group O'N (ON)
- 11. Harada-Norton group HN or F5+ or F5
- 12. Lyons group Ly
- 13. Thompson group Th or F3|3 or F3
- 14. Baby Monster group B or F2+ or F2
- 15. Fischer-Griess Monster group M or F1
- (Undecidedly) the Tits group, 2F4(2)′.
These are often called the "happy family", a name affectionately coined by Robert Griess, who was one of the leading mathematicians on the ongoing research project about sporadic groups at the time. There are 6 exceptions to the happy family, the "pariahs", namely being J1, J3, J4, O'N, Ru, and Ly.