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
Keywords
Examples
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
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
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).
Programs
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GAP
A054396 := Filtered([1..2015], n -> NumberSmallGroups(n) = 4); # Muniru A Asiru, Nov 04 2017
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Mathematica
Select[Range[500], FiniteGroupCount[#] == 4 &] (* Jean-François Alcover, Dec 08 2017 *)
Formula
Sequence is { m | A000001(m) = 4 }. - Muniru A Asiru, Nov 04 2017
Extensions
More terms from Christian G. Bower, May 25 2000