Gravity theories are constructed on finite groups G. A self-consistent review
of the differential calculi on finite G is given, with some new developments.
The example of a bicovariant differential calculus on the nonabelian finite
group S_3 is treated in detail, and used to build a gravity-like field theory
on S_3.Comment: LaTeX, 26 pages, 1 figure. Corrected misprints and formula giving
exterior product of n 1-forms. Added note on topological actio