  Any quantum system with a non-trivial Hamiltonian is able to simulate any
other Hamiltonian evolution provided that a sufficiently large group of unitary
control operations is available. We show that there exist finite groups with
this property and present a sufficient condition in terms of group characters.
We give examples of such groups in dimension 2 and 3. Furthermore, we show that
it is possible to simulate an arbitrary bipartite interaction by a given one
using such groups acting locally on the subsystems.
