

A054396


Numbers n such that there are precisely 4 groups of order n.


22



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..369
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 { k  A000001(k) = 4 }.  Muniru A Asiru, Nov 04 2017


EXAMPLE

For n = 28, the 4 groups of order 8 are C7 : C4, C28, D28, C14 x C2 and for n = 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 &] (* JeanFrançois Alcover, Dec 08 2017 *)


PROG

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


CROSSREFS

Cf. A000001, A003277, A054395, A054397, A055561, A054396, A135850.
Sequence in context: A042622 A044977 A046466 * A083274 A067913 A116566
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



