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GroupTheory

 HigmanSimsGroup

 Calling Sequence HigmanSimsGroup()

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{HigmanSimsGroup}\left(\right)$
 ${G}{≔}{\mathbf{HS}}$ (1)
 > $\mathrm{Degree}\left(G\right)$
 ${100}$ (2)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${44352000}$ (3)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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