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Mathematics of Computation

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ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Irreducible finite integral matrix groups of degree $8$ and $10$
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by Bernd Souvignier PDF
Math. Comp. 63 (1994), 335-350 Request permission


The lattices of eight- and ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in $\mathrm {GL}_n(\mathbb {Z})$ 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 $\mathrm {GL}_8(\mathbb {Z})$, resp. $\mathrm {GL}_{10}(\mathbb {Z})$. 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.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 335-350
  • MSC: Primary 20H15; Secondary 11E12, 20C10, 20C40
  • DOI:
  • MathSciNet review: 1213836