Metacyclic group

In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. That is, it is a group "G" for which there is a short exact sequence
where "H" and "K" are cyclic. Equivalently, a metacyclic group is a group "G" having a cyclic normal subgroup "N", such that the quotient "G"/"N" is also cyclic.
Properties.
Metacyclic groups are both supersolvable and metabelian.