A294156 Numbers m such that there are precisely 15 groups of order m.

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

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