nLab Conway group



Group Theory

Exceptional structures



The Conway groups, Co 1,Co 2,Co 3Co_{1}, Co_{2}, Co_{3}, are three of the sporadic finite simple groups. A fourth group, Co 0Co_0, is the group of automorphisms of the Leech lattice with respect to addition and inner product. This latter group is not simple, but Co 1Co_1 is the quotient group of Co 0Co_0 by its center of order 2. The other two simple Conway groups are subgroups of Co 1Co_1.

The simple Conway groups are three of the seven members of the ‘second generation’ of the Happy Family of 20 simple subquotients of the Monster group.


As automorphism group of super VOAs

The Conway group Co 0Co_{0} is the group of automorphisms of a super VOA of the unique chiral N=1 super vertex operator algebra of central charge c=12c = 12 without fields of conformal weight 1/21/2

(Duncan 05, see also Paquette-Persson-Volpato 17, p. 9)

See also at moonshine.



See also


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