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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. 2

%I

%S 60,168,360,504,660,1092,2448,2520,3420,4080,5616,6048,6072,7800,7920,

%T 20160,20160,25920,62400,95040,126000,181440,443520,604800,979200,

%U 1451520,1814400,3265920,4245696,10200960

%N The orders, with repetition, of the non-cyclic finite simple groups that are subquotients of the automorphism groups of sublattices of the Leech lattice.

%C Note: not every sublattice of the Leech lattice is necessarily a section of the Leech lattice. For example, every Niemeyer lattice is commensurable with the Leech lattice; thus the orders of the simple components of their automorphism groups are in this list, even when those groups are not sections of Co0.

%C By a theorem of Conway and Sloane, any simple group with a cover that has a crystallographic representation in <= 21 dimensions is in this list.

%C This is a subsequence of A330583.

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.

%D J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer, 3rd ed., 1999.

%H Hal M. Switkay, <a href="/A330584/b330584.txt">Table of n, a(n) for n = 1..56</a>

%H J. H. Conway, N. J. A. Sloane, <a href="https://doi.org/10.1098/rspa.1989.0124">Low-dimensional lattices V: Integral coordinates for integral lattices</a>, Proc. Royal Soc. A 426 (1989), 211-232.

%H David A. Madore, <a href="http://www.madore.org/~david/math/simplegroups.html">Orders of non-abelian simple groups</a>

%H R. A. Wilson et al., <a href="http://brauer.maths.qmul.ac.uk/Atlas/v3/">ATLAS of Finite Group Representations - Version 3</a>

%e 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.

%Y Cf. A109379, A080683, A330583.

%K nonn,fini,full

%O 1,1

%A _Hal M. Switkay_, Dec 18 2019

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Last modified September 28 03:06 EDT 2020. Contains 337392 sequences. (Running on oeis4.)