The 501st Legion (also known as "Vader's Fist") is a fictional Clone Trooper (and later Stormtrooper) unit from the Star Wars movies and Expanded Universe. They served under Darth Vader, and were considered to be the best soldiers in the galaxy. Most of the story linked to the 501st comes from the game Star Wars: Battlefront II.
The Legion's name is based on a fan organization of the same name; their inclusion in the official continuity was based on the worldwide organization's dedication to Star Wars fandom.
The 501st Legion, like all Clone Troopers and Clone Trooper Legions, was created on Kamino. They were cloned from the genetic samples provided by famed bounty hunter, Jango Fett, and bred to serve as part of the Grand Army of the Republic. They served in the first actions of the Clone Wars, and were the only legion to assault the Jedi Temple. They appeared identical to the 1.25 million clone units created by the Kaminoans. However, the actions of the 501st, as well as the 65th Homeworld Security Shocktrooper Legion under the command of Thire, became the center of special interest from the Supreme Chancellor Palpatine during the Battle of Geonosis. During the Clone Wars, one team of Clones from the 501st was led by Captain Rex (an ARC Trooper captain who led the Torrent squad of the 501st and reported directly to General Skywalker).
Both Legions were transferred to a secret facility on Coruscant, where they were retrained in advanced infantry, commando, and space-combat techniques. The 501st Legion was kept on Coruscant until the Battle of Jabiim highlighted the level of threat the CIS posed to the Galactic Republic. In response to this, Palpatine authorized the 'release' of members and squads of the 501st to other Clone forces, in order to spread their specialist skills amongst the fronts of the Clone Wars. These clones were absorbed into their new Legions, but a record of each clone's location was kept in secret, so that the entire Legion could be pulled back together when necessary. Some clones were sent in small detachments to serve in space battles.
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