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

Author

Muniru A Asiru, Oct 23 2017

Keywords

• nonn

Examples

			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.
		

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

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).

Programs

GAP

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

Extensions

More terms from Muniru A Asiru, Nov 18 2017