The present invention regards a group for supporting and tightening a rim of or for a tired wheel, and such group includes a base, a wheel-holder table, an upright or column projecting upward from the base and supporting at the top the wheel-holder table, a shaft or pin mounted in or alongside the upright or column, a sleeve element or ring nut element constrainable or mountable on the shaft or pin and means for the relative movement of the shaft or pin and of the table.