Crystals with formula (TMMC) consist of infinite linear chains, running along the c axis, composed of manganese atoms bridged by three chlorine atoms and of disordered (TMA) located in spaces between the chains. The hexagonal structure at room temperature (space group with Z = 2) is characterized by an orientational disorder of the organic group TMA. A weakly first-order phase transition occurs at 126 K which stabilizes a monoclinic low-temperature phase (space group with Z = 4). The crystal structure of TMMC has been studied at 8 K and 295 K by means of powder neutron diffraction experiments. It is shown that this phase transition is characterized by an antiphase translational displacement of the infinite linear chains along the hexagonal axis which couples with an orientational ordering process of the TMA groups. This latter process can be described in the frame of a complex Frenkel model involving reorientations of the TMA groups, in the room-temperature phase, over six energetically equivalent potential wells.