A330584 The orders, with repetition, of the non-cyclic finite simple groups that are subquotients of the automorphism groups of sublattices of the Leech lattice.
60, 168, 360, 504, 660, 1092, 2448, 2520, 3420, 4080, 5616, 6048, 6072, 7800, 7920, 20160, 20160, 25920, 62400, 95040, 126000, 181440, 443520, 604800, 979200, 1451520, 1814400, 3265920, 4245696, 10200960
Offset: 1
Examples
All simple groups of order less than 9828 have crystallographic representations within sublattices of the Leech lattice. The smallest nontrivial crystallographic representation of L2(27), of order 9828, is 26-dimensional.
References
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
- J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer, 3rd ed., 1999.
Links
- Hal M. Switkay, Table of n, a(n) for n = 1..56
- J. H. Conway, N. J. A. Sloane, Low-dimensional lattices V: Integral coordinates for integral lattices, Proc. Royal Soc. A 426 (1989), 211-232.
- David A. Madore, Orders of non-abelian simple groups
- R. A. Wilson et al., ATLAS of Finite Group Representations - Version 3
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