The Thompson group of order $90745943887872000$ is one of the sporadic finite simple groups.  It can be realized as the centralizer of an element of order $3$ in the Monster.

The ThompsonGroup() command returns a symbolic representation of the Thompson group.

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

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

$G≔\mathrm{ThompsonGroup}\left(\right)$

$G≔Th$

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

$90745943887872000$

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

${\left(2\right)}^{15}{\left(3\right)}^{10}{\left(5\right)}^3{\left(7\right)}^2\left(13\right)\left(19\right)\left(31\right)$

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

$\mathrm{true}$

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

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