Sounds like either True Talents or possibly Hidden Talents, both by David Lubar.
Part of the description for Hidden Talents mentions their abilities
However, as Martin gets to know better this Ragtag Bunch of Misfits, he starts to notice that something's unusual about his friends: all five appear to have psychic abilities. Although they initially disbelieve him, even to the point of ostracizing him when he persists in his theory that they are not delinquents as the rest of the world presumes, Martin manages to make them accept their gifts.
It also mentions that they are in a correctional facility.
The first book follows the adventures of Martin, a smart-aleck sent to Edgeville Alternative School, a correctional facility.
The Goodreads synopsis for True Talents explains the powers a bit better:
Trash can move things with his mind, Torchie is a fire-starter, Cheater reads minds, Lucky finds lost objects, Flinch can predict the future, and Martin can see into people’s souls.
The description for True Talents specifically mentions them being referred to as "The Psychic Six"
A year and a half after the events of the first book, Eddie "Trash" Thalmeyer wakes up from a drugged stupor in a cell, having lost his memories of the past six months. After escaping, he finds himself lost in Philadelphia, and learns that the people who abducted him to study his telekinetic abilities also faked his death. Now he must find his friends, find a way home, and find a way to stop the man chasing him from bringing all of the Psychic Six under his thumb.