nLab Conway group

Idea

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

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.

Properties

As automorphism group of super VOAs

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

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

See also at moonshine.

References

General

See also

• Wikipedia, Conway group

Moonshine

• John F. Duncan, Super-moonshine for Conway’s largest sporadic group (arXiv:math/0502267)

• Natalie Paquette, Daniel Persson, Roberto Volpato, BPS Algebras, Genus Zero, and the Heterotic Monster (arXiv:1701.05169)