In Athens, the ship’s captain was known as the trierarch (triērarchos). He was a wealthy Athenian citizen (usually from the class of the pentakosiomedimoi), responsible for manning, fitting out and maintaining the ship for his liturgical year at least; the ship itself belonged to Athens. The triērarchia was one of the liturgies of ancient Athens; although it afforded great prestige, it constituted a great financial burden, so that in the 4th century, it was often shared by two citizens, and after 397 BC it was assigned to special boards.
Source: Wikipedia