Extremely unorthodox in design, the ship was twice the size of a Constitution-class starship, had a hull composed of crystalline ceramic, and was capable of achieving at least warp 3. The ship was also surrounded by an immense energy field that could project the visage of Kukulkan.
The ship contained Kukulkan's zoo, and the machinery to create virtual worlds in the minds of other cognizant beings. It was also equipped with a powerful probe beam, and transporters that could penetrate deflector shields. Offensive capabilities of the ship included the ability to create a force globe to restrict the movement of its target.
Encounter with the Federation
Kulkulkan's ship was encountered by the USS Enterprise in 2270, while investigating an alien probe that had visited and scanned several Federation homeworlds. During the encounter, several members of the Enterprise crew were beamed aboard the vessel.
In an attempt to distract Kukulkan, Captain Kirk released a Capellan power-cat. The cat caused damage to the ship severe enough to cause Kukulkan to lose control of it. (TAS: "How Sharper Than a Serpent's Tooth")