A367463 - OEIS

A367463

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

%I #6 Nov 19 2023 02:00:13

%S 1,2,3,4,5,6,8,9,10,12,16,18,20,24,32,36,40,48,60,64,72,96,120,128,

%T 144,192,240,288,384,576,1152

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

%C 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.

%H J. H. Conway and N. J. A. Sloane, <a href="http://neilsloane.com/doc/Me146.pdf">Low-dimensional lattices. II. Subgroups of GL(n,Z)</a>, Proc. R. Soc. Lond. A 419 (1988), 29-68.

%Y Cf. A018261.

%K nonn,fini,full

%O 1,2

%A _Hal M. Switkay_, Nov 18 2023