Sirius IV

Sirius IV was a planet colonised by humans. By the year 2540, however, it had become a planet within the Earth Empire.

As a dominion, Sirius IV had great autonomy within the Empire; it dealt with Earth mostly as an equal. once used this special status as a way to negotiate for the release of the Third Doctor and Jo Grant into his custody. By fabricating charges against them on Sirius IV, he was able to successfully argue that he had greater claim to the prisoners than Earth Security.

General Williams took a dismissive view of Sirius IV's dominion status. (TV: Frontier in Space)

Behind the scenes
According to the novelisation the planet was called "Alderberan Four", and it had only recently become a dominion.