A066115 -id:A066115 - cp's OEIS frontend

A066113 a(n) is the number of conjugacy classes of maximal subgroups of the alternating group A_n.

0, 1, 2, 3, 5, 5, 6, 8, 7, 7, 11, 9, 9, 11, 12, 10, 13, 10, 14, 14, 13, 13, 19, 15, 15, 18, 20, 15, 21, 20, 22, 20, 18, 21, 27, 19, 21, 21, 27, 21, 27, 22, 26, 29, 24, 24, 32, 27, 31, 27, 31, 27, 33, 30, 35, 34, 30, 30, 41, 31, 33, 40, 40, 41, 40, 34, 39, 36, 40

Offset: 2

Reiner Martin, Dec 30 2001

nonn

Andrew Howroyd, Table of n, a(n) for n = 2..250
M. W. Liebeck, C. E. Praeger and J. Saxl, A classification of the maximal subgroups of the finite alternating and symmetric groups, J. Algebra 111(1987), no. 2, 365-383; Math. Rev. 89b:20008.

Cf. A029726, A066115, A316435.

List([2..50],i->Length(MaximalSubgroupClassReps(AlternatingGroup(i))));

More terms from Alexander Hulpke, Feb 19 2002

Terms a(51) and beyond from Andrew Howroyd, Jul 02 2018

A290138 Number of maximal subgroups of the symmetric group S_n.

Original entry on oeis.org

0, 1, 4, 8, 22, 53, 184, 353, 1376, 3977, 363904, 396498, 39920896, 40060127, 1543910, 4687418, 1307674433536, 1307902407753, 355687428358144, 355691118382364, 162615882312376736, 1267150213999727, 51090942171713634304, 51090956256672365547

Offset: 1

James Mitchell and Wilf A. Wilson, Jul 21 2017

nonn

a(n) + 1, n > 1, is the number of maximal subsemigroups of each of the following monoids of degree n: the full transformation monoid, the symmetric inverse monoid, the dual symmetric inverse monoid, the uniform block bijection monoid, and the Brauer monoid.
a(n) + 2 is the number of maximal subsemigroups of the partial transformation monoid of degree n.
a(n) + 3, n > 1, is the number of maximal subsemigroups of the partial Brauer monoid of degree n.
a(n) + 4, n > 1, is the number of maximal subsemigroups of the partition monoid of degree n.

Wilf A. Wilson, Table of n, a(n) for n = 1..84
Utsithon Chaichompoo and Kritsada Sangkhanan, Transformation Semigroups Which Are Disjoint Union of Symmetric Groups, arXiv:2411.15081 [math.RA], 2024. See p. 10.
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.

Cf. A066115.

Sum(List(ConjugacyClassesMaximalSubgroups(SymmetricGroup(n)), Size));

cp's OEIS Frontend

A066113 a(n) is the number of conjugacy classes of maximal subgroups of the alternating group A_n.

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