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A000638 Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n.
(Formerly M1244 N0477)
1, 1, 2, 4, 11, 19, 56, 96, 296, 554, 1593, 3094, 10723, 20832, 75154, 159129, 686165, 1466358, 7274651 (list; graph; refs; listen; history; text; internal format)



F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 147.

Labelle, Jacques. "Quelques especes sur les ensembles de petite cardinalité."Ann. Sc. Math. Québec 9.1 (1985): 31-58.

G. Pfeiffer, Counting Transitive Relations, preprint 2004.

C. C. Sims, Computational methods in the study of permutation groups, pp. 169-183 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=0..18.

A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079.

A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079. [Annotated scan of page 1069 only]

L. Naughton and G. Pfeiffer, Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group, arXiv preprint arXiv:1211.1911, 2012. - From N. J. A. Sloane, Jan 02 2013

G. Pfeiffer, Subgroups

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

C. C. Sims, Letter to N. J. A. Sloane (no date)

N. J. A. Sloane, Transforms

G. Xiao, PermGroup

Index entries for sequences related to groups


Euler Transform of A005226. Define b(n), c(n), d(n): b(1)=d(1)=0. b(k)=A005227(k), k>1. c(k)=a(k), k>0, d(k)=A005226(k), k>1. d is Dirichlet convolution of b and c. - Christian G. Bower, Feb 23 2006


(MAGMA) n := 5; #SubgroupLattice(Sym(n));

(GAP 4r2) Length(ConjugacyClassesSubgroups(SymmetricGroup(n)));


Partial sums of A000637.

Cf. A000001, A000019. Unlabeled version of A005432.

Sequence in context: A018674 A076518 A139785 * A039824 A204519 A076636

Adjacent sequences:  A000635 A000636 A000637 * A000639 A000640 A000641




N. J. A. Sloane.


a(11) corrected and a(12) added by Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004

Extended to a(18) using Derek Holt's data from A000637. - N. J. A. Sloane, Jul 31 2010



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Last modified May 25 07:12 EDT 2016. Contains 273273 sequences.