The milky way galaxy is huge by any measurement.

It is a barred spiral galaxy some 30,000 to 35,000 parsecs in diameter and is, on average, about 300 parsecs thick.which contains about 350-400 billion stars. The Imperial Core is located within the disk, about 8000 parsecs away from the Galactic Center(The fastest imperial ship would take 5 1/2 years to get to the middle), on a spiral-shaped concentration of gas and dust called the Orion Arm. The stars in the inner 3,000 parsecs form a bulge and one or more bars that radiate from the bulge. The very center is marked by an intense radio source named Sagittarius A which is likely to be a supermassive black hole.

The area claimed by the Empire is about 1/4000 to 1/5000 of the total galactic volume depending on the cut off point in star density one wants to make.

With the area claimed by the empire marked in red