The Ceph Warship was a giant extragalactic Ceph "warship" that appeared in Crysis 3. However, while it was classified as a "warship" by NAX and C.E.L.L. The ship itself is a single and living Ceph among many of the overhive at the fringe of M33 galaxy that sent it.
The Ceph Warship is by far the largest known vessel of the Crysis series. The Ceph Warship is roughly 1/25 the size of Earth (at least 510 km in width and the length is many times longer). The most distinct feature of the Warship is that it possesses giant tentacles giving it a bio-mechanical look similar to that of the Ceph Spaceship. It uses a high-power energy beam as its main weapon.
At the end when Prophet uses the Archangel orbital satellite-weapon platform, you can see the beam charging in the middle of the vessel. If you wait long enough or fail at hacking the satellite's controls, the Ceph Warship will fire and obliterate Earth's surface in one shot, leaving the planet intact so the Ceph can colonize it.
The destruction of the Warship at the hand of Archangel is only thanks to the Nanosuit 2's energy, which basically is Ceph Energy that would triggered exotic catastrophe chain reactions when making contact with any Ceph technology. That explains why instead of being damaged by the Archangel, multiple white holes tore apart its body inside out and the Warship self-destruct on its own, its subsequent detonation annihilates the hundred kilometers white hole that connected to the orbit on the planet where it came from in the M33 galaxy.
The Ceph Warship appears at the very end of Crysis 3 when the Alpha Ceph opens the wormhole to the M33 Galaxy where the Ceph's homeworld is located. It was meant to bring warrior caste - Cephs dedicated purely to warfare - to completely annihilate any and all species that stands in the Ceph's way. At least two of warship will come there as vanguard to obliterate any resistance while the "true" invasion fleet consists dozen vessels will arrive afterward.
The Ceph Warship is destroyed when Prophet takes control of C.E.L.L.'s orbital satellite weapon Archangel and uses it to destroy the Warship by triggering an exotic chain reaction when Ceph Energy making contact with Ceph technology, that causes the Warship to be hollowed inside out by multiple gigantic (at least dozen kilometers for each) and self-destruct on its own instead, resulting a large explosion that covered the entire planet Earth, if not, then at least the northern hemisphere in space.