  A consistent gauging of maximal supergravity requires that the T-tensor
transforms according to a specific representation of the duality group. The
analysis of viable gaugings is thus amenable to group-theoretical analysis,
which we explain and exploit for a large variety of gaugings. We discuss the
subtleties in four spacetime dimensions, where the ungauged Lagrangians are not
unique and encoded in an E_7(7)\Sp(56,R)/GL(28) matrix. Here we define the
T-tensor and derive all relevant identities in full generality. We present a
large number of examples in d=4,5 spacetime dimensions which include
non-semisimple gaugings of the type arising in (multiple) Scherk-Schwarz
reductions. We also present some general background material on the latter as
well as some group-theoretical results which are necessary for using computer
algebra.
