The personal flagship of Darth Vader, the Executor, is the Empire's first Super-class Star Destroyer. The Executor is over eight times the size of an Imperial-class Star Destroyer.
Such ships could be considered overkill, since a smaller vessel could fulfill its specific duties as a headquarters ship. But it effectively symbolizes the Emperor's unlimited power and resources.
The Executor is presented to Lord Vader shortly after the Battle of Yavin. It carries more than 1,000 weapons; two full wings of 144 TIE fighters and 200 other combat and support ships; 38,000 ground stormtroopers; and enough garrison bases and Imperial walkers to destroy any Rebel base.
Vader directs the hunt for Luke Skywalker and the pursuit of the Rebels aboard the Executor, communicating holographically with the Emperor and striding the walkways of the command bridge above the work stations of his officers.