2-adic cofiltration of SO3(Q)

We prove that the group SO3(Q) of rational rotations is the inverse limit of a family of finite solvable groups of order 23k−2⋅3, whose 2-Sylow subgroups have nilpotency class 2k−3, exponent 2k−1, and Frattini subgroups coinciding with the commutator subgroups, and we give generators for these groups.