Future applications of discotic liquid crystals (DLCs) in electronic devices depend on a marked improvement of their conductivity properties. We present a study of 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT6) and show how local conformation, structural defects, and thermal motions on the picosecond time scale strongly affect the efficient charge transport in DLCs. A direct and successful comparison of classical molecular dynamics (MD) simulations with both neutron powder diffraction and quasielastic neutron scattering (QENS) give a full insight into the structural and dynamical properties of HAT6. The local conformation of HAT6 molecules is characterized by a mutual rotation (twist) angle of about 37 degrees and typically a mutual aromatic-core distance of 3.4 angstrom instead of the average distance of 3.65 angstrom usually quoted. We show that a considerable number of structural traps is present in HAT6, which persist at the picosecond time scale. We find that the high disorder in the mutual positions of the aromatic cores is an important factor contributing to the limited conductivity of HAT6 compared to larger DLCs.