---
tag: TNPQ9AWVBC
kind: object
name: Baby Monster group
msc: [20D08]
uses: [PZ49Z4CBFZ, 0YMYMNQ0QZ, 0B85S2V2DR, C9VY20TAPT, 02YYV36BFM]
sources:
  - url: https://en.wikipedia.org/wiki/Baby_monster_group
same_as:
  wikidata: Q797816
  wikipedia: Baby monster group
---

## Description

The Baby Monster group $\mathbb{B}$ is the second largest of the $26$ [[sporadic groups|PZ49Z4CBFZ]].
It is a finite [[simple group|0YMYMNQ0QZ]] of [[order|0B85S2V2DR]]
$$\abs{\mathbb{B}} = 2^{41} \cdot 3^{13} \cdot 5^6 \cdot 7^2 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 31 \cdot 47,$$
which is $4154781481226426191177580544000000$, about $4 \cdot 10^{33}$.

## Remarks

The Baby Monster was found by Bernd Fischer.
It is a subquotient of the [[Monster group|C9VY20TAPT]]: the Monster contains an involution whose [[centraliser|02YYV36BFM]] is a double cover $2 \cdot \mathbb{B}$ of the Baby Monster.
The smallest nontrivial irreducible complex representation of $\mathbb{B}$ has dimension $4371$.

## Explanations

### L1 human

The Baby Monster is the second largest exceptional finite simple group.
It sits inside the Monster.
The elements of the Monster that commute with a certain element of order $2$ form, up to a factor of $2$, a copy of the Baby Monster.