Union of Allied Planets
The Union of Allied Planets (usually just called "the Alliance") is the governing power of the star system that is the setting for the Firefly series.
The exact nature of the Alliance government isn't clear, but it appears to be a kind of oligarchy run by wealthy families and powerful corporations. Its chief legislative body is a Parliament.
The Alliance has a fleet of warships, some comparable to cities in size. Many are multi-role ships capable of directly engaging other warships and deploying starfighters. Their speed, power resources, and firepower are all unspecified.
While they control a large star system with numerous colonized planets and moons, the Alliance has no faster-than-light propulsion technology, limiting their influence to their home system. This limitation makes them a negligible threat to interstellar civilizations.