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%I #25 Dec 26 2023 08:32:14
%S 60,168,360,504,660,1092,2448,2520,3420,4080,5616,6048,6072,7800,7920,
%T 9828,12180,14880,20160,20160,25308,25920,29120,32736,34440,39732,
%U 51888,58800,62400,74412,95040,102660,113460,126000,150348
%N Orders of non-cyclic simple groups (with repetition).
%C The first repetition is at 20160 (= 8!/2) and the first proof that there exist two nonisomorphic simple groups of this order was given by the American mathematician Ida May Schottenfels (1869-1942). - _David Callan_, Nov 21 2006
%C By the Feit-Thompson theorem, all terms in this sequence are even. - _Robin Jones_, Dec 25 2023
%D See A001034 for references and other links.
%H David A. Madore, <a href="/A109379/b109379.txt">Table of n, a(n) for n = 1..493</a> [taken from link below]
%H David A. Madore, <a href="http://www.eleves.ens.fr:8080/home/madore/math/simplegroups.html">More terms</a>
%H John McKay, <a href="http://dx.doi.org/10.1080/00927877908822410">The non-abelian simple groups g, |g|<10^6 - character tables</a>, Commun. Algebra 7 (1979) no. 13, 1407-1445.
%H Ida May Schottenfels, <a href="https://www.jstor.org/stable/1967281">Two Non-Isomorphic Simple Groups of the Same Order 20,160</a>, Annals of Math., 2nd Ser., Vol. 1, No. 1/4 (1899), pp. 147-152.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Feit%E2%80%93Thompson_theorem">Feit-Thompson theorem</a>.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%Y Cf. A000001, A000679, A005180, A001228, A060793, A056866, A056868, A119630.
%Y Cf. A001034 (orders without repetition), A119648 (orders that are repeated).
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_, Jul 29 2006