Central product of UT(3,3) and Z9

Definition
This group can be defined in the following equivalent ways:


 * 1) It is the central product of defining ingredient::prime-cube order group:U(3,3) (which is a non-abelian group of order 27 and exponent 3) and defining ingredient::cyclic group:Z9, where they share a common central subgroup of order three.
 * 2) It is the central product of defining ingredient::semidirect product of Z9 and Z3 (which is a non-abelian group of order 27 and exponent 9) and defining ingredient::cyclic group:Z9, where they share a common central subgroup of order three.