  For finite metabelian 3-groups M with elementary bicyclic commutator quotient
M/M' = C3*C3, coclass cc(M) in {4,6}, and transfer kernel type F, the smallest
Schur sigma-groups S with second derived quotient S/S" = M are determined.
Evidence is provided of arithmetical realizations of these groups by second
3-class groups M = Gal(F(3,2,K)/K), respectively 3-class field tower groups S =
Gal(F(3,infty,K)/K), of imaginary quadratic number fields K=Q(sqrt{d}).
