Math 2.0

Group theory and generalizations Classification of finite simple groups Object

Baby Monster group

Builds on Sporadic groupSimple groupOrder of a groupMonster groupCentraliser

Description

The Baby Monster group 𝔹\mathbb{B} is the second largest of the 2626 sporadic groups. It is a finite simple group of order βˆ£π”Ήβˆ£=241β‹…313β‹…56β‹…72β‹…11β‹…13β‹…17β‹…19β‹…23β‹…31β‹…47,\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 41547814812264261911775805440000004154781481226426191177580544000000, about 4β‹…10334 \cdot 10^{33}.

Remarks

The Baby Monster was found by Bernd Fischer. It is a subquotient of the Monster group: the Monster contains an involution whose centraliser is a double cover 2⋅𝔹2 \cdot \mathbb{B} of the Baby Monster. The smallest nontrivial irreducible complex representation of 𝔹\mathbb{B} has dimension 43714371.

Reading path

To understand this page from the ground up, read these 9 pages in order. The foundations come first.

Show the path as a graph
Centraliser, concept, no evidence levelCentraliserconceptGriess algebra, object, no evidence levelGriess algebraobjectIrreducible representation, concept, no evidence levelIrreducible represent…conceptOrder of a group, concept, no evidence levelOrder of a groupconceptSimple group, concept, no evidence levelSimple groupconceptSporadic group, concept, no evidence levelSporadic groupconceptj-invariant, concept, no evidence levelj-invariantconceptMonster group, object, no evidence levelMonster groupobjectBaby Monster group, object, no evidence levelBaby Monster groupobject
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Centraliser concept
  2. Griess algebra object
  3. Irreducible representation concept
  4. Order of a group concept
  5. Simple group concept
  6. Sporadic group concept
  7. j-invariant concept
  8. Monster group object
  9. Baby Monster group object

Further reading

  1. Web https://en.wikipedia.org/wiki/Baby_monster_group
About this page
TagTNPQ9AWVBC
URIm2://TNPQ9AWVBC
Kindobject
WritingW0 stub
MSC20D08
UsesSporadic group, Simple group, Order of a group, Monster group, Centraliser
Same as
Changed2 November 2026

Markdown Β· JSON Β· Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)
  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.