Monster group

In math, there are many subjects. One of these is group theory. In group theory, the Monster group (shortened to M or F1) is important. It is also called the Fischer-Griess Monster, or the Friendly Giant. It is a group of a finite number of elements, which is equal to:

   808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000
 = 246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 
 ≈ 8 · 1053.

It is a simple group. Simple groups are very important in group theory. They are not made out of other groups, and other groups are always made out of combinations of them. A normal subgroup is an important part of a group. Simple groups have no normal subgroups except the unimportant identity element, and themselves. 

The finite simple groups  have been completely classified (the classification of finite simple groups). There are two kinds of finite simple groups in the list of finite simple groups. The first kind has 18 countably infinite families. The second kind has 26 sporadic groups. They are not as systematic. The Monster group is the largest of these sporadic groups. It contains all but six of the other sporadic groups inside of it. Robert Griess has called these six exceptions pariahs. The rest make up the happy family.

Other websites
 MathWorld: Monster Group
 Atlas of Finite Group Representations: Monster group

Category:Group theory