A298911 Numbers m such that there are precisely 20 groups of order m.

820, 1220, 1530, 2020, 2070, 2610, 2756, 3366, 3620, 4230, 4550, 4770, 4820, 5310, 5620, 5742, 5950, 6370, 6650, 7038, 7470, 8010, 8020, 8050, 8118, 8164, 8330, 8420, 8874, 9220, 9306, 9310, 9316, 9630, 10170, 10420, 10494, 10820, 11050

Offset

1,1

Links

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..237

H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups

Index entries for sequences related to groups

Formula

Sequence is { m | A000001(m) = 20 }.

Example

For m = 820, the 20 groups are (C41 : C5) : C4, C4 x (C41 : C5), C41 x (C5 : C4), C5 x (C41 : C4), C205 : C4, C820, (C41 : C5) : C4, C2 x ((C41 : C5) : C2), C2 x C2 x (C41 : C5), C5 x (C41 : C4), C41 x (C5 : C4), C205 : C4, C205 : C4, C205 : C4, C205 : C4, D10 x D82, C10 x D82, C82 x D10, D820, C410 x C2 where C, D mean the Cyclic, Dihedral groups of the stated order and the symbols x and : mean direct and semidirect products respectively.

Maple

with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 20 then print(n); fi; od;

Crossrefs

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (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), this sequence (k=20).

Sequence in context: A043805 A043813 A043822 * A279796 A285022 A037999

Adjacent sequences: A298908 A298909 A298910 * A298912 A298913 A298914

Keyword

nonn

Author

Muniru A Asiru, Jan 28 2018

Status

approved