Stephane Javelle discovered IC 4588 = J. 3-1391 on 15 Jul 1903 and noted "vF, vS, R, stellar, 5051 p.". His position is a very good match with PGC 57025.
The NGC has a typo "[NGC] 5051 p", instead of "[NGC] 6051 p." The MCG, PGC, HyperLeda, SIMBAD (as well as Megastar, etc.) incorrectly equate IC 4588 with NGC 6051. The correct identification is given in NED, NGC 2000.0 and the Deep Sky Field Guide.
600/800mm - 24" (7/23/14): very faint, very small, round, 10" diameter. Located 2' SE of NGC 6051 and 1.5' E of a mag 11.2 star in the cluster AWM 4.
Notes by Steve Gottlieb