In the mathematical field of group theory, the Monster group M or F_1 (also known as the Fischer-Griess Monster, or the Friendly Giant) is a group of finite order
2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
= 808017424794512875886459904961710757005754368000000000
≈ 8 · 10^53.
It is a simple group, meaning it does not have any normal subgroups except for the subgroup consisting only of the identity element, and M itself.
The finite simple groups have been completely classified (the classification of finite simple groups). The list of finite simple groups consists of 18 countably infinite families, plus 26 sporadic groups that do not follow such a systematic pattern. The Monster group is the largest of these sporadic groups and contains all but six of the other sporadic groups as subquotients. These six exceptions are known as pariahs, and the others as the happy family.
Reference:
http://en.wikipedia.org/wiki/Monster_group
