  We present algorithmic improvements for fast and memory-efficient use of
discrete spatial symmetries in Exact Diagonalization computations of quantum
many-body systems. These techniques allow us to work flexibly in the reduced
basis of symmetry-adapted wave functions. Moreover, a parallelization scheme
for the Hamiltonian-vector multiplication in the Lanczos procedure for
distributed memory machines avoiding load balancing problems is proposed. We
demonstrate that using these methods low-energy properties of systems of up to
50 spin-1/2 particles can be successfully determined.
