Kar-Karthack is the capital of Karthack, a great city crowned by a black citadel.
The Black Citadel is a massive towering fortress atop a massive towering rock in the middle of the Lake of Kar-Karthack. The fortress is gargantuan. Unassailable. Any attack would have to climb up hundreds of feet of stairs or hillside under fire from the parapets before smashing through the fortress's three concentric walls and breaking into its keep, which is itself the size of a large Voscan castle.
On top of this, it is also where the Silver Guards quarter themselves, meaning that outside of specially enhanced rooms, it's terminally cold.