Baby Monster group

Group theory

Group theory Basic notions Subgroup Normal subgroup Quotient group Group homomorphism (semi-)direct product Discrete groups Classification of finite simple groups Cyclic group Zn Alternating group An Sporadic groups Mathieu group M11..12,M22..24 Conway group Co1..3 Janko group J1, 2, 3, 4 Fischer group F22..24 Baby Monster group B Monster group M Other finite groups Symmetric group, Sn Dihedral group, Dn Infinite groups The integers, Z Modular groups, PSL(2,Z) and SL(2,Z) Continuous groups Lie group General linear group GL(n) Special linear group SL(n) Orthogonal group O(n) Special orthogonal group SO(n) Unitary group U(n) Special unitary group SU(n) Symplectic group Sp(n) G2 F4 E6 E7 E8 Lorentz group Poincaré group Infinite dimensional groups conformal group diffeomorphism group Loop group Quantum group O(∞) SU(∞) Sp(∞)

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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

• MathWorld: Baby monster group
• Atlas of Finite Group Representations: Baby Monster group