When you cycle over to the Ships part of the menu screen, you will notice that there are quite a few different ships that you can unlock. One of which is the Executor Ship
Unfortunately the Executor Ship is not flyable, it is merely a random encounter. However, you can go inside the ship and explore. You can even try to seize the ship from enemy hands.
In order to be able to find this ship you can choose to purchase the rumour for it. You will then learn that you can find this ship in either Bespin or Tatooine.
So head to either Bespin or Tatooine space and fly around and hopefully you will come across the Executor encounter.
When you do come across the Executor head towards it to begin the Seize the Executor objective. Our goal now is to destroy the ship defences. This will include TIE Fighters and turrets.
After the defences have been wiped out we can then board the Executor and perform the takeover procedure. This will require us to find and eliminate General Rothlan.
Once General Rothlan has been successfully defeated you can then purchase the Executor Ship for 5,000,000 Shiny Studs