Baby monster group

In the area of modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order

   4,154,781,481,226,426,191,177,580,544,000,000
= 241 · 313 · 56 · 72 · 11 · 13 · 17 · 19 · 23 · 31 · 47
≈ 4×1033.
For the South Korean girl group, see BabyMonster.
Algebraic structure → Group theory
Group theory
Basic notions
  • Subgroup
  • Normal subgroup
Group homomorphisms
Finite groups
  • Schur multiplier
Classification of finite simple groups
Modular groups
  • PSL(2, )
  • SL(2, )
Topological and Lie groups
  • Special linear SL(n)
  • Orthogonal O(n)
  • Special orthogonal SO(n)
  • Unitary U(n)
  • Special unitary SU(n)
  • Symplectic Sp(n)
Infinite dimensional Lie group
  • O(∞)
  • SU(∞)
  • Sp(∞)
Algebraic groups
  • Linear algebraic group
  • Reductive group

B is one of the 26 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 outer automorphism group is trivial and the Schur multiplier has order 2.

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