Sporadic groups

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.

Category:Group theory