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Treaty of Armens

Galaxy-class starship classification mentioned in the Treaty of Armens from 2255

The Galaxy-class starship was a class of Starfleet vessel mentioned in the Treaty of Armens from 2255. It was stated in the treaty, that a UFP official from the Cultural Contact Office (Sol Sector) shall be on board a Galaxy-class Starfleet vessel at all times except during legal holidays.

There were at least two classes named Galaxy-class; the other was in operation a century later. (TNG: "The Ensigns of Command" display graphic)

It is not known when this class operated, but they likely existed before 2255, as that was the last time the Sheliak contacted the Federation, which presumably means the Treaty of Armens is older yet.
A 23rd century Starfleet Galaxy-class starships, also known as Galaxy ships (β) were mentioned in several novels including Dreadnought! and the novelizations of Star Trek: The Wrath of Khan and Star Trek III: The Search for Spock. They were smaller than the Constitution-class, but much faster and designed for very-long-range exploration.