Baby Monster group

In the mathematical field of group theory, the Baby Monster group "B" (or just "Baby Monster") is a group of order

: 2⁴¹ · 3¹³ · 5⁶ · 7² · 11 · 13 · 17 · 19 · 23 · 31 · 47: = 4154781481226426191177580544000000: ≈ 4 · 10³³.

It is a "simple group", meaning it does not have any normal subgroups except for the subgroup consisting only of the identity element, and "B" itself.

The Baby Monster group is one of the sporadic groups, and has the second highest order of these, with the highest order being that of the Monster group. The double cover of the Baby Monster is the centralizer of an element of order 2 in the Monster group.

The smallest faithful matrix representation of the Baby Monster is of size 4370 over the finite field of order 2.

External links

* [http://mathworld.wolfram.com/BabyMonsterGroup.html MathWorld: Baby monster group]
* [http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/B/ Atlas of Finite Group Representations: Baby Monster group]