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A294155 Numbers k such that there are precisely 14 groups of order k. 5
16, 36, 40, 104, 232, 296, 351, 424, 488, 808, 872, 1125, 1192, 1197, 1256, 1384, 1448, 1576, 1755, 1832, 2152, 2216, 2223, 2331, 2344, 2536, 2625, 2792, 2984, 3112, 3176, 3368, 3688, 3861, 4072, 4328, 4329, 4456, 4599, 4875, 4904, 5115, 5187, 5224, 5288, 5301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..377

H. U. Besche, B. Eick and E. A. O'Brien. The Small Groups Library

Gordon Royle, Numbers of Small Groups

Index entries for sequences related to groups

EXAMPLE

For n = 16, the 14 groups of order 16 are C16, C4 x C4, (C4 x C2) : C2, C4 : C4, C8 x C2, C8 : C2, D16, QD16, Q16, C4 x C2 x C2, C2 x D8, C2 x Q8, (C4 x C2) : C2, C2 x C2 x C2 x C2  and for n = 36 the 14 groups of order 36 are C9 : C4, C36, (C2 x C2) : C9, D36, C18 x C2, C3 x (C3 : C4), (C3 x C3) : C4, C12 x C3, (C3 x C3) : C4, S3 x S3, C3 x A4, C6 x S3, C2 x ((C3 x C3) : C2), C6 x C6 where C, D, Q  mean Cyclic group, Dihedral group, Quaternion group of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semi-direct products respectively.

PROG

(GAP) A294155 := Filtered([1..2015], n -> NumberSmallGroups(n) = 14);

CROSSREFS

Cf. A000001, A003277, A054395,  A054396, A054397, A055561, A135850, A249550, A249551, A249552, A249553, A249554, A249555, A292896, A294156.

Sequence in context: A250432 A183196 A109287 * A330869 A334538 A066112

Adjacent sequences:  A294152 A294153 A294154 * A294156 A294157 A294158

KEYWORD

nonn

AUTHOR

Muniru A Asiru, Oct 24 2017

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)