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

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• more

Comments

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

Links

• 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

Crossrefs

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

Programs

GAP

# GAP 4.2
Length(ConjugacyClassesSubgroups(AlternatingGroup(n)));

Magma

n := 5; #SubgroupLattice(Alt(n));

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