Characteristically metacyclic group

Definition
A group is termed characteristically metacyclic if it has a fact about::cyclic characteristic subgroup such that the quotient group is also a cyclic group.

Stronger properties

 * Weaker than::Cyclic group
 * Weaker than::Group with metacyclic derived series

Weaker properties

 * Stronger than::Metacyclic group
 * Stronger than::Polycyclic group
 * Stronger than::Characteristically polycyclic group
 * Stronger than::Supersolvable group

Facts

 * Characteristically metacyclic and commutator-realizable implies abelian