Metacyclic group

Symbol-free definition
A metacyclic group is a group having a defining ingredient::cyclic normal subgroup with a cyclic quotient group.

Definition with symbols
A group $$G$$ is termed metacyclic if there exists a normal subgroup $$N$$ of $$G$$ such that both $$N$$ and $$G/N$$ are cyclic.

Facts

 * Classification of metacyclic p-groups