For a positive integer n, the NumSimpleGroups( n ) command returns the number of simple groups of order n.

For each prime integer n, the number of simple groups of order n is equal to $1$. By the Feit-Thompson Theorem, if n is an odd composite integer, there are no simple groups of order n. The Artin-Tits theorem asserts that the number of simple groups of any given finite order is at most equal to $2$. Therefore, the value returned by NumSimpleGroups( n ), for any positive integer n, is one of $0$, $1$ or $2$.

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

$\mathrm{NumSimpleGroups}\left(1\right)$

$0$

$\mathrm{NumSimpleGroups}\left(13\right)$

$1$

$\mathrm{NumSimpleGroups}\left(15\right)$

$0$

$\mathrm{NumSimpleGroups}\left(360\right)$

$1$

$\mathrm{NumSimpleGroups}\left(20160\right)$

$2$

The GroupTheory[NumSimpleGroups] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.