  We investigate the properties of S=1/2 Heisenberg clusters with random
frustration using exact diagonalizations. This is a model for a quantum spin
glass. We show that the average ground state spin is $S \propto \sqrt{N}$,
where N is the number of sites. We also calculate the magnetic susceptibility
and the spin stiffness and low-energy excitations, and discuss these in terms
of a semiclassical picture.
