The Thrasymachus was a Galaxy class luxury liner operated by the Solaris World Holidays company. It was the largest in the Solaris World Holiday fleet, with a capacity of four thousand passengers.
Amy Pond and Rory Williams found a brochure for the Thrasymachus at a travel agent's on Drago 14 in 2698, entitled Play Among the Stars, and Come Aboard the Thrasymachus. According to it, the Thrasymachus boasted a replica of an Earth tropical resort, Neo-Latin dance lessons, organised space walks, a fun park for young children, a honeymoon suite with a package tour to nearby moons, fine dining by the famed TV star Gourmandroid X7, McLintock's Candy Burgers outlets, a 1953-style fast food bar where one could "tear up [one's] Space War II ration book", and live music by the bio-calypso band Flaming Bongos. (PROSE: Honeymoon Horrors)
In 4398, it entered the cloud belt of the planet Ember controlled by the Sardick family. It was at risk of crashing and Kazran Sardick was prepared to let it do so. However, the Eleventh Doctor convinced him to allow the ship to land on the planet and Amy, Rory (who were in the honeymoon suite before the ship began to crash) and the rest of the crew and passengers were saved. (TV: A Christmas Carol)