A054396 Numbers m such that there are precisely 4 groups of order m.

28, 30, 44, 63, 66, 70, 76, 92, 102, 117, 124, 130, 138, 154, 170, 172, 174, 182, 188, 190, 230, 236, 238, 246, 266, 268, 275, 279, 282, 284, 286, 290, 315, 316, 318, 322, 332, 354, 370, 374, 387, 412, 418, 426, 428, 430, 434, 442, 465, 470, 494, 495, 498

Offset

1,1

Links

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..10000 (terms 1..369 from Muniru A Asiru).

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

Formula

Sequence is { m | A000001(m) = 4 }. - Muniru A Asiru, Nov 04 2017

Example

For m = 28, the 4 groups of order 8 are C7 : C4, C28, D28, C14 x C2 and for m = 30 the 4 groups of order 30 are C5 x S3, C3 x D10, D30, C30 where C, D mean cyclic, dihedral groups of the stated order and S is the symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - Muniru A Asiru, Nov 04 2017

Mathematica

Select[Range[500], FiniteGroupCount[#] == 4 &] (* Jean-François Alcover, Dec 08 2017 *)

Prog

(GAP) A054396 := Filtered([1..2015], n -> NumberSmallGroups(n) = 4); # Muniru A Asiru, Nov 04 2017

Crossrefs

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), this sequence (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), A298909 (k=18), A298910 (k=19), A298911 (k=20).

Sequence in context: A044977 A046466 A374008 * A384684 A083274 A067913

Adjacent sequences: A054393 A054394 A054395 * A054397 A054398 A054399

Keyword

nonn

Author

N. J. A. Sloane, May 21 2000

Extensions

More terms from Christian G. Bower, May 25 2000

Status

approved