The Held group of order $4030387200$ is one of the sporadic finite simple groups. It was discovered by Dieter Held in 1969 as a group containing an involution whose centralizer is isomorphic to the centralizer of an involution in the Mathieu group $M_{24}$.  (The only other such group is the group $PSL\left(5\,2\right)$ .) The construction of the Held group was later completed by Graham Higman and John McKay. The Held group can also be realized as the centralizer of an element of order $7$ in the Monster.

The HeldGroup() command returns either a permutation group, or a finitely presented group, isomorphic to the Held group.

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

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

$G≔\mathrm{HeldGroup}\left(\right)$

$G≔\mathbf{He}$

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

$2058$

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

$4030387200$

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

$\mathrm{true}$

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

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