A218966 Number of conjugacy classes of subgroups of the symmetric which are also subgroups of the alternating group.

1, 1, 1, 2, 5, 9, 22, 37, 112, 195, 423, 780, 2401, 4409

Offset

0,4

Links

Table of n, a(n) for n=0..13.

GAP, GAP package TomLib, The GAP Library of Tables of Marks.

Liam Naughton, CountingSubgroups.g

Liam Naughton and Goetz Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013.

Liam Naughton and Goetz Pfeiffer, Tomlib, The GAP table of marks library.

Prog

(GAP)
# GAP 4.11.1
n := 9;;
GS := List( [1..n], m-> SymmetricGroup(m));;
subS := List( GS, x-> ConjugacyClassesSubgroups(x));;
repS := List( subS, x-> List(x, Representative));;
GA := List( [1..n], m-> AlternatingGroup(m));;
List( [1..n], m-> Number( repS[m], x-> IsSubgroup( GA[m], x)));
# Peter Dolland, Jul 15 2021

Crossrefs

Sequence in context: A303963 A304349 A024822 * A029726 A052962 A173565

Adjacent sequences: A218963 A218964 A218965 * A218967 A218968 A218969

Keyword

nonn,more

Author

Liam Naughton, Nov 23 2012

Status

approved