Fischer group Fi24
In the area of modern algebra known as group theory, the Fischer group Fi24 or F24′ is a sporadic simple group of order
History and properties
Fi24 is one of the 26 sporadic groups and is the largest of the three Fischer groups introduced by Bernd Fischer (1971, 1976) while investigating 3-transposition groups. It is the 3rd largest of the sporadic groups (after the Monster group and Baby Monster group).
The outer automorphism group has order 2, and the Schur multiplier has order 3. The automorphism group is a 3-transposition group Fi24, containing the simple group with index 2.
The centralizer of an element of order 3 in the monster group is a triple cover of the sporadic simple group Fi24, as a result of which the prime 3 plays a special role in its theory.
Representations
The centralizer of an element of order 3 in the monster group is a triple cover of the Fischer group, as a result of which the prime 3 plays a special role in its theory. In particular it acts on a vertex operator algebra over the field with 3 elements.