The Conway groups ${\mathrm{Co}}_1$, ${\mathrm{Co}}_2$ and ${\mathrm{Co}}_3$ are sporadic finite simple groups, discovered by John H. Conway in the 1960s.

The largest Conway group ${\mathrm{Co}}_1$ is the quotient of the automorphism group of the Leech lattice (a certain $24$-dimensional unimodular lattice) by its center (of order $2$), and has order equal to $4157776806543360000$.

The second Conway group ${\mathrm{Co}}_2$ has order equal to $42305421312000$, and is the group of automorphisms of the Leech lattice fixing a vector of length $2$.

The third Conway group ${\mathrm{Co}}_3$ has order equal to $495766656000$, and can be described as the group of automorphisms of the Leech lattice fixing a vector of length $\sqrt{6}$.

The ConwayGroup( n ) command returns a permutation group isomorphic to the Conway group ${\mathrm{Co}}_n$, for n = 1,2,3.

In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{ConwayGroup}\left(2\right)$

$G≔{Co}_2$

$\mathrm{Degree}\left(G\right)$

$2300$

$\mathrm{GroupOrder}\left(G\right)$

$42305421312000$

$\mathrm{IsSimple}\left(G\right)$

$\mathrm{true}$

The GroupTheory[ConwayGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.