The Talos star group was a star cluster in the Milky Way Galaxy named after the Talosian planetary system. It was located in the third quadrant of the vernal galaxy between Rigel VII and the Vega colony, approximately six days away from Starbase 11 for a Constitution-class starship traveling at maximum warp.
By the mid-23rd century, the cluster was unexplored and was not the site of any colonies. The only expedition into the region, a survey by the SS Columbia, had culminated in the Columbia disappearing under mysterious circumstances in 2236. Eighteen years later, in 2254, the USS Enterprise, under the command of Captain Christopher Pike, on a search-and-recovery mission for survivors of the downed survey ship became the second ship to enter the star group. (TOS: "The Cage", "The Menagerie, Part I")
Background information Edit
The image of the Talos star group was a color astrophotographic exposure of M45, the Pleiades Cluster. The exposure was relatively short, and so was lacking detail of the characteristic Merope Nebula. However, the nebula does give a blue halo to the stars visible within the photograph.
The vernal galaxy information comes from the "For eyes of Starfleet Command only" file read by Kirk in "The Menagerie, Part I". It was unknown what the vernal galaxy was, exactly, and how its quadrants are arranged. This reference system was never used again. Dialog in "The Cage" clearly states Earth and Talos to be in the same galaxy. According to Pike, the Enterprise originated from a stellar group at the other end of the galaxy relative to Talos. According to the "The Explored Galaxy" star chart, Talos was however located relatively close to Earth. According to the chart, it was also located between the Tholian Assembly and Romulus. Both of were identified in DS9: "Call to Arms" as Alpha Quadrant powers.
According to the Star Trek: Star Charts (pgs. 34, "United Federation of Planets III"), the Talos Star Group was located in or near Federation space, in the Alpha Quadrant.