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A054396 Numbers n such that there are precisely 4 groups of order n. 22

%I

%S 28,30,44,63,66,70,76,92,102,117,124,130,138,154,170,172,174,182,188,

%T 190,230,236,238,246,266,268,275,279,282,284,286,290,315,316,318,322,

%U 332,354,370,374,387,412,418,426,428,430,434,442,465,470,494,495,498

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

%H Muniru A Asiru, <a href="/A054396/b054396.txt">Table of n, a(n) for n = 1..369</a>

%H H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://www.icm.tu-bs.de/ag_algebra/software/small/">The Small Groups Library</a>

%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F Sequence is { k | A000001(k) = 4 }. - _Muniru A Asiru_, Nov 04 2017

%e 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

%t Select[Range[500], FiniteGroupCount[#] == 4 &] (* _Jean-Fran├žois Alcover_, Dec 08 2017 *)

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

%Y Cf. A000001, A003277, A054395, A054397, A055561, A054396, A135850.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 21 2000

%E More terms from _Christian G. Bower_, May 25 2000

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Last modified September 29 08:29 EDT 2020. Contains 337428 sequences. (Running on oeis4.)