A367463 The orders, without repetition, of the subquotients of finite groups with irreducible representations in GL_4(Z).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 32, 36, 40, 48, 60, 64, 72, 96, 120, 128, 144, 192, 240, 288, 384, 576, 1152

Offset: 1

Author

Hal M. Switkay, Nov 18 2023

Keywords

• nonn
• fini
• full

Comments

Conway and Sloane identify 5 conjugacy classes of maximal finite irreducible subgroups of GL_4(Z). Of these, 2 are isomorphic to subgroups of other groups in the list. The 3 maximal groups are: 1) the Weyl group of F4, the automorphism group of the D4 lattice, with order 1152; 2) the wreath square of the dihedral group of order 12, the automorphism group of the (A2)^2 lattice, with order 288; 3) the product of the symmetric group of degree 5 with the group of order 2, the automorphism group of the A4 lattice (and its dual), with order 240.

Links

• J. H. Conway and N. J. A. Sloane, Low-dimensional lattices. II. Subgroups of GL(n,Z), Proc. R. Soc. Lond. A 419 (1988), 29-68.

Crossrefs

Cf. A018261.