Dalek Supreme Command

A Dalek Supreme of the Dalek Council represented Dalek Supreme Command. He travelled in a spacecraft (TV: Planet of the Daleks) designated as Councillor-class. (PROSE: The Jeopardy of Solar Proximity)

History
During the 22nd century Dalek invasion of Earth, Dalek Supreme Command ordered that the human rebels were to be crushed. (PROSE: Doctor Who and the Dalek Invasion of Earth)

In the 26th century, a member of the Supreme Council arrived to take command of operations on the planet Spiridon. He exterminated the Dalek Section Leader for its incompetence and ended up stranded after Thals stole his ship, but called for another one. (TV: Planet of the Daleks)

The cure for the Movellan virus was synthesized after Davros' work had been transmitted to Supreme Command. (PROSE: The Secret Lives of Monsters)

Behind the scenes

 * Using the Dalek Earthforce as an example, The Dalek Handbook states that each Dalek-occupied planet was overseen by its own Dalek Supreme Command, directed by a Black Supreme Controller, with the Supreme Command on Skaro being led by the Black Dalek Supreme. Supreme Command is apparently a separate entity from the Dalek Supreme Council, which The Dalek Handbook claims was only established following the Dalek Civil War.