Q was established sometime within and or before the year 2006. During that year, they attempted to assassinate the Star Plasma Vessel in order to achieve their goals. They had hoped to stop Master Tengen from resetting their cursed technique, believing they would evolve into an enemy of humanity and Jujutsu High.
The location of the Star Plasma Vessel was leaked and members of Q were the first people there. After an explosion close to the top floor of a tall building, Kokun of Q throws Riko Amanai out the window in hopes that she'll be killed by the fall. Jujutsu student, Suguru Geto ends up rescuing her, prompting Kokun to engage him.
Down below, Suguru's partner Satoru Gojo watches the commotion. He's attacked by Bayer, Q's strongest soldier. Bayer is aware of Satoru's famous abilities and decides to fight him Both Kokun and Bayer are effortlessly defeated by the special grade sorcerers and the organization is forced to disband.