The USS Vengeance was an alternate reality Federation Dreadnought-class starship under the command of Admiral Alexander Marcus in 2259. The Vengeance was built in secret by Section 31 in orbit of Jupiter in order to prepare for war with the Klingon Empire. The vessel was designed by Khan under the pseudonym Commander John Harrison. (ST movie: Star Trek Into Darkness)
The USS Vengeance was constructed following the destruction of Vulcan in secret by Section 31 at the Io Facility. There, Admiral Marcus put Lieutenant John Harrison on it to make everything from the propulsion to the weapons system better. In five months, Harrison was able to give the warp drive more unprecedented capability up to warp 10. (TOS - Khan comic: "Issue 4")
After the terrorist attacks on London and Starfleet Headquarters, Admiral Alexander Marcus ordered James T. Kirk and the crew of the USS Enterprise to pursue John Harrison to the Klingon homeworld. After Harrison's capture, Admiral Marcus used the Vengeance to travel to meet the Enterprise. Finding the ship on the edge of the Klingon Neutral Zone, the Vengeance pursued and opened fire on the Enterprise after Kirk refused to turn over Harrison (who had revealed his true identity as Khan).
The Enterprise attempted to escape the Vengeance by jumping to warp but the Vengeance overtook the Enterprise and knocked it out of warp near Earth. The Vengeance was about to destroy Enterprise after Marcus labeled the crew as traitors and in league with Khan; however, Montgomery Scott was able to disable the Vengeance. Kirk and Khan then space jumped to the Vengeance to rescue Carol Marcus and stop the attack, but Khan tricked Kirk and assumed command of the ship after killing Adm. Marcus. Khan then demanded that Spock, in command of the Enterprise, to return his people, who were cryogenically stored in 72 special long range torpedoes. Spock agreed; however, he removed the other Augments from the torpedoes and activated the warheads. The torpedoes were then beamed aboard the Vengeance where they detonated, crippling the vessel.
As the Vengeance fell to Earth, Khan set it in on a course towards Starfleet Headquarters but was only successful in destroying a part of San Francisco's water front, including the former Alcatraz prison. (TOS movie & novelization: Star Trek Into Darkness)
The Vengeance was a Dreadnought-class starship, designed by Khan Noonien Singh after the lives of his crew were threatened by Starfleet and Section 31. The vessel was two times larger than the Constitution-class of the era and was three times stronger. The ship was heavily automated to the point that she could successfully function with a crew of one person aboard and had more spartan accommodations for personnel than other Federation vessels. The vessel was armed with phaser arrays capable of firing while at warp, multiple torpedo launchers, and other experimental weaponry. She was also faster than other ships of the era and was capable of interfacing with their warp bubble. Its bridge was smaller than contemporary vessels and it featured an expansive shuttle bay and, at minimum, nine hangar bays. (TOS movie & novelization: Star Trek Into Darkness)