A218913 Number of distinct orders of subgroups of the symmetric group.

1, 1, 2, 4, 8, 13, 21, 31, 49, 74, 113, 139, 216, 268

Offset: 0

Author

Liam Naughton, Nov 09 2012

Keywords

• nonn
• more

Links

• L. Naughton and G. Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013 and J. Int. Seq. 16 (2013) #13.5.8
• Liam Naughton, CountingSubgroups.g
• Liam Naughton and Goetz Pfeiffer, Tomlib, The GAP table of marks library,

Programs

GAP

Size(DuplicateFreeList(List(ConjugacyClassesSubgroups(G), x-> Size(Representative (x)))));

Sage

def A218913(n):
    G = SymmetricGroup(n)
    subgroups = G.conjugacy_classes_subgroups()
    return len(set(subG.cardinality() for subG in subgroups))
# Peter Luschny, Apr 21 2016