Starbase 56 was a Federation starbase administered by Starfleet.
In 2369, Starbase 56 was named on a chart titled Sector Ipai Relay Log - Relay Message Flow 1293 in the Relay Station 47 Ops. This base sent a message on Starfleet Commnet Four via a secure channel. One of its missions that year was as a deep space post for Sector 21834. (TNG: "Aquiel", production art)
The starbase's sector's designation was x701. The first number might be a "6" or an "8".