  Anyons obtained from a finite gauge theory have a computational power that
depends on the symmetry group. The relationship between group structure and
computational power is discussed in this paper. In particular, it is shown that
anyons based on finite groups that are solvable but not nilpotent are capable
of universal quantum computation. This extends previously published results to
groups that are smaller, and therefore more practical. Additionally, a new
universal gate-set is built out of an operation called a probabilistic
projection, and a quasi-universal leakage correction scheme is discussed.
