Conway Groups

The automorphism group Co_1 of the Leech lattice modulo a center of order two is called "the" Conway group. There are 15 exceptional conjugacy classes of the Conway group. This group, combined with the groups Co_2 and Co_3 obtained similarly from the Leech lattice by stabilization of the one- and two-dimensional sublattices, are collectively called Conway groups.

The Conway groups are sporadic groups. The are implemented in the Wolfram Language as ConwayGroupCo1[], ConwayGroupCo2[], and ConwayGroupCo3[].

The following table summarizes some properties of the Conway groups, where k indicates the transitivity and L is the length of the minimal permutation support.


See also

Leech Lattice, Sporadic Group

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Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, 1985.Wilson, R. A. "ATLAS of Finite Group Representation."

Referenced on Wolfram|Alpha

Conway Groups

Cite this as:

Weisstein, Eric W. "Conway Groups." From MathWorld--A Wolfram Web Resource.

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