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 A294156 Numbers m such that there are precisely 15 groups of order m. 20
 24, 54, 81, 84, 136, 220, 228, 250, 260, 328, 340, 372, 513, 516, 580, 584, 620, 625, 686, 712, 740, 776, 804, 884, 891, 904, 948, 999, 1060, 1096, 1236, 1375, 1377, 1420, 1460, 1508, 1524, 1544, 1668, 1780, 1812, 1863, 1864, 1911, 1924, 1928, 1940, 1956, 1971, 1972, 2056, 2132, 2180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..1061 H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library Gordon Royle, Small Even Order Groups [archived copy] Index entries for sequences related to groups FORMULA A294156 = { m | A000001(m) = 15 }. - M. F. Hasler, Oct 24 2017 EXAMPLE For m = 24, the 15 groups of order 24 are C3 : C8, C24, SL(2,3), C3 : Q8, C4 x S3, D24, C2 x (C3 : C4), (C6 x C2) : C2, C12 x C2, C3 x D8, C3 x Q8, S4, C2 x A4, C2 x C2 x S3, C6 x C2 x C2 and for n = 54 the 15 groups of order 54 are D54, C54, C3 x D18, C9 x S3, ((C3 x C3) : C3) : C2, (C9 : C3) : C2, (C9 x C3) : C2, ((C3 x C3) : C3) : C2, C18 x C3, C2 x ((C3 x C3) : C3), C2 x (C9 : C3), C3 x C3 x S3, C3 x ((C3 x C3) : C2), (C3 x C3 x C3) : C2, C6 x C3 x C3 where C, D, Q, S, A and SL mean Cyclic, Dihedral, Quaternion, Symmetric, Alternating and Special Linear group. The symbols x and : mean direct and semi-direct products respectively. MATHEMATICA Select[ Range@2000, FiniteGroupCount@# == 15 &] (* Robert G. Wilson v, Oct 24 2017 *) PROG (GAP) A294156 := Filtered([1..2015], n -> NumberSmallGroups(n) = 15); CROSSREFS Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), this sequence (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20). Sequence in context: A084586 A259023 A301575 * A108215 A322609 A234238 Adjacent sequences: A294153 A294154 A294155 * A294157 A294158 A294159 KEYWORD nonn AUTHOR Muniru A Asiru, Oct 24 2017 STATUS approved

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Last modified September 13 03:33 EDT 2024. Contains 375857 sequences. (Running on oeis4.)