A029726 Number of conjugacy classes of subgroups of the alternating group A_n.

1, 1, 1, 2, 5, 9, 22, 40, 137, 223, 430, 788, 2537, 4558, 12136, 24871, 95526, 182234

Offset

0,4

Comments

Number of even permutation groups; also number of molecular species based on even permutation groups. - Christian G. Bower, Feb 23 2006

Links

Table of n, a(n) for n=0..17.

L. Naughton and G. Pfeiffer, Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group, arXiv preprint arXiv:1211.1911, 2012 and J. Int. Seq. 16 (2013) #13.5.8

Götz Pfeiffer, Numbers of subgroups of various families of groups

N. J. A. Sloane, Transforms

Prog

(GAP)
# GAP 4.2
Length(ConjugacyClassesSubgroups(AlternatingGroup(n)));
(Magma) n := 5; #SubgroupLattice(Alt(n));

Crossrefs

Cf. A000001, A000638. Unlabeled version of A029725. Euler transform of A116653.

Sequence in context: A304349 A024822 A218966 * A052962 A173565 A268651

Adjacent sequences: A029723 A029724 A029725 * A029727 A029728 A029729

Keyword

hard,nonn,more

Author

N. J. A. Sloane.

Extensions

More terms from Reiner Martin, Dec 30 2001

a(10)-a(13) added by Christian G. Bower, Feb 23 2006 based on Goetz Pfeiffer's web page.

a(14)-a(17) from Vaclav Kotesovec, Jul 21 2022

Status

approved