Sirius was a star with a solar system roughly 8.6 light years away from Sol. It had (at least) five planets - Sirius Alpha (BFA/BBCR: Max Warp), Androzani Major and Minor (DW: The Caves of Androzani), Sirius IV (DW: Frontier in Space) and Sirius V (DW: City of Death) - colonised and explored by Earth. The corporation Sirius Conglomerate was a major power, and chairman Morgus refered to himself as being the richest man in "the five worlds". (DW: The Caves of Androzani)
In the 26th century, Sirius IV was a dominion planet, partially autonomous from Earth's government. In later centuries, Androzani Major had its own government.