The Higman-Sims group is a sporadic finite simple group of order equal to $44352000$.  It was discovered in 1967 by Donald Higman and Charles Sims as the subgroup of index $2$ in the automorphism group of the Higman-Sims graph. It was independently re-discovered by Graham Higman in 1969.

The HigmanSimsGroup() command returns a permutation group (default), or a finitely presented group, isomorphic to the Higman-Sims group.

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

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

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

$G≔\mathbf{HS}$

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

$100$

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

$44352000$

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

$\mathrm{true}$

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

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