An error estimate for finite volume methods for multidimensional conservation laws

The lattices of eight- and ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in GL_n(Z) for n = 8, 10, are classified in this paper. The number of types is 52 in the case n = 8, and 47 in the case n = 10. As a consequence of this classification one has 26, resp. 46, conjugacy classes of maximal finite irreducible subgroups of GL₈(Z), resp. GL₁₀(Z). In particular, each such group is absolutely irreducible, and therefore each of the maximal finite groups of degree 8 turns up in earlier lists of classifications.