When discovered, it had the highest proper motion of any star known, replacing 61 Cygni in that department. Later it dropped to second place after the discovery of Kapteyn's Star, and still later to third place after the discovery of Barnard's Star. It is considerably farther away than either of those stars, however, which means its transverse velocity is greater.
Actually, it is the Sun which is following the motion of galaxy rotation by revolving around the center of the Milky Way; halo stars like Groombridge 1830 do not follow this galaxy rotation and thus are "standing still" and appear to be moving in "retrograde direction" at high speed.
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