A group $G$ is metacyclic if it is an extension of a cyclic group by another cyclic group.

The IsMetacyclic( G ) command attempts to determine whether the group G is metacyclic.  It returns true if G is metacyclic and returns false otherwise.

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

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

$\mathrm{true}$

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

$\mathrm{false}$

$\mathrm{IsMetacyclic}\left(\mathrm{MetacyclicGroup}\left(3\,2\,3\right)\right)$

$\mathrm{true}$

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

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