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 A137863 Orders of simple groups which are non-cyclic and non-alternating. 2
 168, 504, 660, 1092, 2448, 3420, 4080, 5616, 6048, 6072, 7800, 7920, 9828, 12180, 14880, 20160, 25308, 25920, 29120, 32736, 34440, 39732, 51888, 58800, 62400, 74412, 95040, 102660, 113460, 126000, 150348, 175560, 178920, 194472, 246480, 262080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Bernard Schott, Apr 26 2020: (Start) About a(16) = 20160; 20160 = 8!/2 is the order of the alternating simple group A_8 that is isomorphic to the Lie group PSL_4(2), but, 20160 is also the order of the Lie group PSL_3(4) that is not isomorphic to A_8. Indeed, 20160 is the smallest order for which there exist two nonisomorphic simple groups and it is the order of this group PSL_3(4) that was missing in the data. The first proof that there exist two nonisomorphic simple groups of this order was given by the American mathematician Ida May Schottenfels (1900) [see the link]. (End) REFERENCES L. E. Dickson, Linear groups, with an exposition of the Galois field theory (Teubner, 1901), p. 309. LINKS David Madore, Orders of non abelian simple groups Ida May Schottenfels, Two non isomorphic simple groups of the same order 20160, Annals of Mathematics, Second Series, Vol. 1, No. 1/4 (1900), pp. 147-152. EXAMPLE From Bernard Schott, Apr 27 2020: (Start) Two particular examples: a(1) = 168 is the order of the smallest non-cyclic and non-alternating simple group, this Lie group is the projective special linear group PSL_2(7) that is isomorphic to the general linear group GL_3(2). a(12) = 7920 is the order of the smallest sporadic group (A001228), the Mathieu group M_11. (End) CROSSREFS Cf. A001034, A001710, A005180, A109379. Subsequence: A001228 (sporadic groups). Sequence in context: A247721 A342427 A027679 * A266808 A234738 A234731 Adjacent sequences:  A137860 A137861 A137862 * A137864 A137865 A137866 KEYWORD nonn AUTHOR Artur Jasinski, Feb 16 2008 EXTENSIONS More terms from R. J. Mathar, Apr 23 2009 a(16) = 20160 inserted by Bernard Schott, Apr 26 2020 Incorrect formula and programs removed by R. J. Mathar, Apr 27 2020 Terms checked by Bernard Schott, Apr 26 2020 STATUS approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)