What do you call a union of several peoples under one ruler?

A group of different peoples that are ruled by one ruler or by one government can be called many things. ancient Rome ruled over such a diverse groups of peoples and ancient Rome is called an empire. This was the case with Great Britain until the end of WW 2. India, various island nations and such, like Ireland were all part of the British empire. In other situations a group of diverse peoples are in a nation and are ruled by a government. A case can be made that the US government rules a large number of different peoples. Most of the time, however, that term is not used.