Coulomb breakup of unstable neutron-rich carbon isotopes C-15.17 has been studied at energies around similar to 500600 MeV/nucleon. Non-resonant low-lying dipole strength is observed in these isotopes which can be explained by a direct breakup mechanism. In addition to the decay neutron from excited projectile, gamma-rays emitted from excited fragments after Coulomb breakup are measured in coincidence, giving access to quantitative spectroscopic information. The spectroscopic factor deduced for a valence neutron occupying the S-1/2 level in the C-15 ground state is consistent with that obtained earlier from (d, p) transfer reactions. The analysis for Coulomb breakup of C-17 shows that most of the cross section yields the C-16 core in excited states. The predominant ground-state configuration of C-17 is found to be C-16(2(+)) circle times nu(s,d).