A292896 Numbers m such that there are precisely 13 groups of order m.

56, 60, 150, 189, 441, 726, 837, 945, 1012, 1161, 1204, 1521, 1575, 1647, 1734, 1809, 1988, 2079, 2133, 2205, 2366, 2619, 2781, 2925, 2948, 3174, 3213, 3556, 3610, 3753, 4077, 4239, 4324, 4347, 4851, 5046, 5211, 5697, 5805, 5908, 6021, 6183, 6507, 6692, 7479, 7497, 7605, 7623, 7641, 7749, 8410, 8451

Offset

1,1

Links

Muniru A Asiru, Table of n, a(n) for n = 1..273

Gordon Royle, Numbers of Small Groups

H. U. Besche, B. Eick and E. A. O'Brien. The Small Groups Library

Index entries for sequences related to groups

Example

The 13 groups of order 56 have the following structure C7 : C8, C56, C7 : Q8, C4 x D14, D56, C2 x (C7 : C4), (C14 x C2) : C2, C28 x C2, C7 x D8, C7 x Q8, (C2 x C2 x C2) : C7, C2 x C2 x D14, C14 x C2 x C2 where C, D and Q mean Cyclic group, Dihedral group and Quarternion group of the stated order. The symbols x and : mean direct and semidirect products respectively.

Prog

(GAP) A292896 := Filtered([1..2015], n -> NumberSmallGroups(n) = 13);

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), this sequence (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: A116660 A047727 A069810 * A154768 A165159 A336265

Adjacent sequences: A292893 A292894 A292895 * A292897 A292898 A292899

Keyword

nonn

Author

Muniru A Asiru, Oct 23 2017

Extensions

More terms from Muniru A Asiru, Nov 18 2017

Status

approved