Irreducible Finite Integral Matrix Groups of Degree 8 and 10

Bernd Souvignier
1994 Mathematics of Computation  
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 therefore
more » ... e, and therefore each of the maximal finite groups of degree 8 turns up in earlier lists of classifications.
doi:10.2307/2153579 fatcat:r4vlgvghizga7mzh7nctae6aie