Groups primarily appear as symmetry groups, which play a prominent role in all areas of physics. In classical mechanics and quantum mechanics, these are the rotations and translations in space, or more generally, the elements of the Galilean group. In relativistic physics, these are the Lorentz and Poincaré groups. The point groups of molecular physics are finite subgroups of the rotation group, and the crystal groups of solid state theory are discrete subgroups of the group of rigid motions.