Monster group - Definition and Overview

In mathematics, the Monster group M is a group of order

   2⁴⁶ · 3²⁰ · 5⁹ · 7⁶ · 11² · 13³ · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71

= 808017424794512875886459904961710757005754368000000000

≈ 8 · 10⁵³.

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; there are 18 countably infinite families of finite simple groups, plus 26 sporadic groups that do not follow any apparent pattern. The Monster group is the largest of these sporadic groups. See classification of finite simple groups.

The Monster was predicted by Bernd Fischer and Robert Griess in 1973, and first constructed by Griess in 1980 as the automorphism group of the Griess algebra, a 196883-dimensional commutative nonassociative algebra.

The Monster group prominently features in the Monstrous Moonshine conjecture which relates discrete and non-discrete mathematics and was proven by Richard Borcherds in 1992.