  We develop a systematic method for classifying supersymmetric orbifold
compactifications of M-theory. By restricting our attention to abelian
orbifolds with low order, in the special cases where elements do not include
coordinate shifts, we construct a "periodic table" of such compactifications,
organized according to the orbifolding group (order up to 12) and dimension (up
to 7). An intriguing connection between supersymmetric orbifolds and
G2-structures is explored.
