It should say that Dn/Z(Dn) is isomorphic to D(n/2). I understand your definition for Dn/Z(Dn), but I don't get how to set up the isomorphism. I think I should use the fact that any group generated by a pair of elements of order 2 is dihedral to get the isomorphism from Dn/Z(Dn) to D(n/2) ?