Central product of D8 and Z16

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


 * 1) It is the central product of defining ingredient::dihedral group:D8 and defining ingredient::cyclic group:Z16 over a commonly identified cyclic central subgroup cyclic group:Z2.
 * 2) It is the central product of defining ingredient::quaternion group and defining ingredient::cyclic group:Z16 over a commonly identified cyclic central subgroup cyclic group:Z2.

Description by presentation
gap> F := FreeGroup(3);  gap> G := F/[F.1^4,F.2^2,F.1*F.2*F.1*F.2,F.1^2*F.3^8,F.1*F.3*F.1^(-1)*F.3^(-1),F.2*F.3*F.2^(-1)*F.3^(-1)]; 