She is the first battle cruiser commissioned by the SGC.She is officially known as the BC-303. She is the only ship of her class to be commisioned by the SGC.
Her commanding of officer was Colonel Pentergast. Though General Hammond commanded her in the battle for Antarctica and the first mission to Atlantis.
She led the battle over Antarctica and it was only because of the Heroism of her Captain that SG-1 had enough time to operate the defence platform.
Sadly she was destroyed by the Ori.
Here is some information from Wikipedia(MORE PICTURES AFTER TEXT).
The Prometheus, also known as the BC-303 or the X-303 early in development, is Earth's first capital starship, introduced in the season 6 episode "Prometheus". The original concept for the look of the Prometheus in season 6 was an aircraft carrier. The producers wanted to build something that was exactly the opposite of Goa'uld ships, which according to Paul Mullie are basically big empty rooms with nowhere to sit, no screens, and no buttons to press. Andy Mikita thought the Prometheus was a fun set to shoot in because "there's lots of layers and textures and flashing lights". Much of the inspiration for the X-303's interior came from contemporary American aircraft carriers. Bridget McGuire developed the initial concept based on pictures. Bodnarus developed the blueprints of the X-303 that were shown in "Nightwalkers" before the X-303 made its first appearance in "Prometheus". Art director James Robbins developed the interior schematics and interior workings, while Bodnarus developed the actual set interiors including the bridge, corridors, engine room and air lock.
A hybrid of human and alien technologies, the Prometheus is the product of two years and several billion dollars' worth of development by the United States Air Force. The ship originally features reverse-engineered Goa'uld technologies, including ring transporters and crystal-based control systems. It is also equipped with artificial gravity generators and an inertial dampening system. The corridors are constructed of the fictional metal trinium. Substantial amounts of naqahdah are also used in its construction. In "Disclosure", the Asgard install advanced shields and weapons (though the latter are never seen or mentioned in later episodes) on the unfinished Prometheus as thanks for SG-1's help against the Replicators. In "Covenant", Jack O'Neill asks Thor for a new hyperdrive for the Prometheus, which is installed by the Asgard in "Endgame" along with beaming technology. However, since the Prometheus lacks advanced Asgard sensors, locator beacons are required to target the beams.
The sublight engines of the Prometheus have a top speed of 110,000 miles per second (59% light speed) and can attain orbit from Earth's surface in under thirty seconds. Its original hyperdrive cost 2 billion dollars in research and development and uses naqahdriah as a power source. A buffer was installed to manage the unstable power stream from the naqahdria, but it is overloaded by an unexpected gravity wave on the Prometheus' shakedown cruise. The ship is then fitted with a hyperdrive salvaged from a Goa'uld Al'kesh, but as that engine is designed for a much smaller ship, the Prometheus can only make short jumps with time in between for the drive to cool down. With the new Asgard hyperdrive installed in "Endgame", the Prometheus is able to reach other galaxies. The Prometheus is armed with 4 railguns, a close-in weapons system, and 16 missile batteries. It carries eight F-302s for fighter support.
In its first appearance, the incomplete Prometheus is hijacked by rogue NID agents and subsequently called upon by the Asgard for a mission against the Replicators. In "Memento", the Prometheus, commanded of Colonel William Ronson, is temporarily stranded near Tagrea after its hyperdrive overloads. In "Grace", the Prometheus is attacked by an unknown enemy warship and almost becomes trapped after hiding in an unusual nebula. Under the command of General George Hammond, the Prometheus defends Earth against Anubis' armada in "Lost City". The ship is subsequently commanded by Colonel Lionel Pendergast, except in "Prometheus Unbound" when Hammond briefly reassumes command. In that episode, Vala Mal Doran hijacks the Prometheus, stranding the crew in a disabled Al'kesh. Under Pendergast, the Prometheus conducts missions against Ba'al and the Trust, and against the Ori. In "Ethon", the Prometheus is destroyed by a satellite weapon of Ori design over Tegalus. The last appearance of the ship is in an alternate universe in "The Road Not Taken", where it serves as the equivalent of Air Force One for President Hank Landry.