A group $G$ is almost simple if it has an unique minimal normal subgroup which is a non-Abelian simple group. Alternatively, the group $G$ is almost simple if, up to isomorphism, we have $S\le G$ and $G\le \mathrm{Aut}\left(S\right)$, for a non-Abelian simple group $S$.

The IsAlmostSimple( G ) command returns true if the group G is almost simple, and returns false otherwise.

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

$\mathrm{IsAlmostSimple}\left(\mathrm{MathieuGroup}\left(10\right)\right)$

$\mathrm{true}$

$\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(3\right)\right)$

$\mathrm{false}$

$\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(4\right)\right)$

$\mathrm{false}$

$\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(5\right)\right)$

$\mathrm{true}$

$\mathrm{IsAlmostSimple}\left(\mathrm{Symm}\left(6\right)\right)$

$\mathrm{true}$

$\mathrm{IsAlmostSimple}\left(\mathrm{PSL}\left(2\,5\right)\right)$

$\mathrm{true}$

$\mathrm{IsAlmostSimple}\left(\mathrm{CyclicGroup}\left(11\right)\right)$

$\mathrm{false}$

The GroupTheory[IsAlmostSimple] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.