So, all this grinding of the mission "Assimilation" got me curious enough to google the catalogue number while waiting for the replay cooldown to wear off.
Turns out it's actually a distant Galaxy.
http://dso-browser.com/dso/info/NGC/4447
Who knew we're THAT far away from home.

NGC-2447 (which is right next to it on the sector map), on the other hand, is an open star cluster within the Milky Way so at least that one is within the realm of possibility (even though the 3600 LY distance is pushing it).
Comments
Star Trek Battles member. Want to roll with a good group of people regardless of fleets and not have to worry about DPS while doing STFs? Come join the channel and join in the fun!
http://forum.arcgames.com/startrekonline/discussion/1145998/star-trek-battles-channel-got-canon/p1
My character Tsin'xing
I'm fairly confident that even transwarp gateways only lead to other places within the Milky Way. In Star Trek canon, very few Federation ships have even been outside the Milky Way, let alone to distant galaxies.
There used to be a picture here, but they changed signatures and I can't be bothered to replace it.
they are all labeled NGC in game... they MAY have meant FGC but accidently used the Real code instead.