The thermodynamics of a conductive liquid is considered. The latter is described within the framework of contact geometry. The state and constitutive equations of the medium are obtained from the first principles and notion of symmetry under natural assumptions only. These thermodynamic relations are supplemented by the general laws of charge, mass, momentum, and energy conservation to form a complete system of partial differential equations that describe the motion of the media. Differential invariants of this system under the action of rotations and translations are studied. A complete set of such invariants is obtained.