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The lattices of eight-and ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in GL"(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. GLio(Z) . In particular, each such group is absolutely irreducible, and thereforedoi:10.2307/2153579 fatcat:r4vlgvghizga7mzh7nctae6aie