GroupTheory

Description

 • The Harada-Norton group of order $273030912000000$ is one of the sporadic finite simple groups.  It was discovered independently by Koichi Harada in 1976, and by Simon Norton in 1975, using different methods.  It can be described as a centralizer of an element of order $5$ in the Monster.
 • The HaradaNortonGroup() command returns a symbolic group representing the Harada-Norton group.
 • In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{HaradaNortonGroup}\left(\right)$
 ${G}{≔}{\mathbf{HN}}$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${273030912000000}$ (2)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (3)

Compatibility

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