Paste the class list and split it into groups, either a number of groups or a size per group. Big enough to read off the board while everyone moves.
Paste the register, choose whether you are fixing the number of groups or the number of people in each, and press shuffle. Leftovers are spread across the groups rather than dumped into a last small one, so you do not end up with a group of one.
Shuffle again if the room reacts badly to a pairing. It takes a second and it is fairer than overruling it by hand, because the class watched it happen.
Learnify turns the class into a role-playing game run from the teacher's screen: points for real reasons, avatars that evolve, attendance, groups and quiz games. Pupils need no devices and no accounts of their own.