  We re-examine the quantization of structure constants, or equivalently the
choice of lattice in the so-called flat group reductions, introduced originally
by Scherk and Schwarz. Depending on this choice, the vacuum either breaks
supersymmetry and lifts certain moduli, or preserves all supercharges and is
identical to the one obtained from the torus reduction. Nonetheless the
low-energy effective theory proposed originally by Scherk and Schwarz is a
gauged supergravity that describes supersymmetry breaking and moduli lifting
for all values of the structure constants. When the vacuum does not break
supersymmetry, such a description turns out to be an artifact of the consistent
truncation to left-invariant forms as illustrated for the example of ISO(2). We
furthermore discuss the construction of flat groups in d dimensions and find
that the Scherk--Schwarz algorithm is exhaustive. A classification of flat
groups up to six dimensions and a discussion of all possible lattices is
presented.
