The automorphism group 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 and 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 indicates the transitivity and is the length of the minimal permutation support.

group | order | factorization | ||

2 | 276 | 495766656000 | ||

1 | 2300 | 42305421312000 | ||

1 | 98280 | 4157776806543360000 |