Finite Simple Groups
The finite simple groups have been classified into a number of series as well as 26 sporadic groups. Of these, 20 are subgroups or subquotients of the monster group, referred to as the "Happy Family", while 6 are not, and are referred to as "pariahs".
Several of the sporadic groups are related to the Leech lattice, most notably the Conway group Co1, which is the automorphism group of the Leech lattice, quotiented out by its center.
Read more about this topic: Exceptional Object
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