Commutator-realizable group

Definition
A group is termed commutator-realizable if it can be realized as the defining ingredient::commutator subgroup of some group.

Stronger properties

 * Weaker than::Perfect group
 * Weaker than::Cyclic group

Facts

 * Characteristically metacyclic and commutator-realizable implies abelian

Metaproperties
If $$G$$ is commutator-realizable, and $$H$$ is a characteristic subgroup of $$G$$, $$G/H$$ is also a commutator-realizable group.