A298909 Numbers m such that there are precisely 18 groups of order m.

156, 342, 444, 666, 732, 876, 930, 1164, 1308, 1314, 1830, 1884, 1962, 2172, 2286, 2316, 2748, 2892, 2934, 3258, 3324, 3582, 3675, 3756, 4044, 4125, 4188, 4422, 4476, 4530, 4764, 4878, 4908, 4970, 5050, 5052, 5196, 5430, 5445, 5481, 5484, 5526, 6330, 6492, 6822, 6924

Offset

1,1

Links

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..283

H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups

Index entries for sequences related to groups

Formula

Sequence is { m | A000001(m) = 18 }.

Example

For m = 156, the 18 groups are (C13 : C4) : C3, C4 x (C13 : C3), C13 x (C3 : C4), C3 x (C13 : C4), C39 : C4, C156, (C13 : C4) : C3, C2 x ((C13 : C3) : C2), C3 x (C13 : C4), C39 : C4, S3 x D26, C2 x C2 x (C13 : C3), C13 x A4, (C26 x C2) : C3, C6 x D26, C26 x S3, D156, C78 x C2 where C, D mean Cyclic, Dihedral groups of the stated order and S, A mean the Symmetric, Alternating groups of the stated degree. The symbols x and : mean direct and semidirect products respectively.

Maple

with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 18 then print(n); fi; od;

Prog

(GAP) Filtered([1..2015], n -> NumberSmallGroups(n) = 18);

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), A294156 (k=15), A295161 (k=16), A294949 (k=17), this sequence (k=18), A298910 (k=19), A298911 (k=20).

Sequence in context: A166397 A065709 A037983 * A366172 A156849 A250382

Adjacent sequences: A298906 A298907 A298908 * A298910 A298911 A298912

Keyword

nonn

Author

Muniru A Asiru, Jan 28 2018

Status

approved