In mathematics, the Baby Monster groupB (or just Baby Monster) is a group of order
241 313 56 72 11 13 17 19 23 31 47
= 4154781481226426191177580544000000
≈ 4 1033.
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 in fact a subgroup of the Monster group.
The smallest faithful matrix representation of the Baby Monster is of size 4370 over the finite field of order 2.
The typical example of a 3-transposition group is a symmetric group, where the Fischer transpositions are genuinely transpositions.
The groups he found fell into several infinite classes (as well as the symmetric groups, certain classes of symplectic and orthogonal groups fulfilled his conditions) with the exception of the three Fischer groups.
It is the 3rd largest of the sporadic groups (after the Monstergroup and BabyMonstergroup).
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