Fischer group Fi23

In the area of modern algebra known as group theory, the Fischer group Fi₂₃ is a sporadic simple group of order

Fi₂₃ is one of the 26 sporadic groups and is one the three Fischer groups introduced by Bernd Fischer (1971, 1976) while investigating 3-transposition groups.

The Schur multiplier and the outer automorphism group are both trivial.

The Fischer group Fi₂₃ has a rank 3 action on a graph of 31671 vertices corresponding to 3-transpositions, with point stabilizer the double cover of the Fischer group Fi22. It has a second rank-3 action on 137632 points

The smallest faithful complex representation has dimension 782. The group has an irreducible representation of dimension 253 over the field with 3 elements.

Conway and Norton suggested in their 1979 paper that monstrous moonshine is not limited to the monster, but that similar phenomena may be found for other groups. Larissa Queen and others subsequently found that one can construct the expansions of many Hauptmoduln from simple combinations of dimensions of sporadic groups. For Fi₂₃, the relevant McKay-Thompson series is ${\displaystyle T_{3A}(\tau )}$ where one can set the constant term a(0) = 42 ( ),

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