A group $G$ is quasi-simple if it is perfect and its central quotient is simple. In particular, every simple non-abelian group is quasi-simple.

The IsQuasisimple( G ) command returns true if the group G is quasi-simple, and returns false otherwise.

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

$\mathrm{IsQuasisimple}\left(\mathrm{TrivialGroup}\left(\right)\right)$

$\mathrm{false}$

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

$\mathrm{false}$

$\mathrm{IsQuasisimple}\left(\mathrm{GL}\left(2\,4\right)\right)$

$\mathrm{false}$

$\mathrm{IsQuasisimple}\left(\mathrm{SL}\left(2\,5\right)\right)$

$\mathrm{true}$

$\mathrm{IsQuasisimple}\left(\mathrm{SL}\left(2\,7\right)\right)$

$\mathrm{true}$

$\mathrm{IsQuasisimple}\left(\mathrm{PerfectGroup}\left(1920\,3\right)\right)$

$\mathrm{false}$

$\mathrm{IsQuasisimple}\left(\mathrm{PSO}\left(-1\,4\,5\right)\right)$

$\mathrm{true}$