cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A378279 Number of subgroups of S_n isomorphic to S_3, where S_n is the n-th symmetric group.

Original entry on oeis.org

0, 0, 1, 4, 20, 160, 910, 5936, 53424, 397440, 3304620, 35023120, 322852816
Offset: 1

Views

Author

Jianing Song, Nov 21 2024

Keywords

Crossrefs

Column k=3 of A378163.

Programs

  • GAP
    A378279 := function(n)
    local S;
    S := SymmetricGroup(n);
    return Sum(IsomorphicSubgroups(S, SymmetricGroup(3)), x->Index(S, Normalizer(S, Image(x))));
    end;

Formula

a(n) = (A281097(n) - A000085(n))/6. See A378163 for more information.

A378280 Number of subgroups of S_n isomorphic to S_4, where S_n is the n-th symmetric group.

Original entry on oeis.org

0, 0, 0, 1, 5, 60, 560, 5740, 58716, 734160, 8337120, 133212420, 1769490580
Offset: 1

Views

Author

Jianing Song, Nov 21 2024

Keywords

Crossrefs

Column k=4 of A378163.

Programs

  • GAP
    A378280 := function(n)
    local S;
    S := SymmetricGroup(n);
    return Sum(IsomorphicSubgroups(S, SymmetricGroup(4)), x->Index(S, Normalizer(S, Image(x))));
    end; # See A378163

A378281 Number of subgroups of S_n isomorphic to S_5, where S_n is the n-th symmetric group.

Original entry on oeis.org

0, 0, 0, 0, 1, 12, 84, 560, 3276, 79632, 1105104, 16571808, 176344740
Offset: 1

Views

Author

Jianing Song, Nov 21 2024

Keywords

Crossrefs

Column k=5 of A378163.

Programs

  • GAP
    A378281 := function(n)
    local S;
    S := SymmetricGroup(n);
    return Sum(IsomorphicSubgroups(S, SymmetricGroup(5)), x->Index(S, Normalizer(S, Image(x))));
    end;

A281097 Number of group homomorphisms S_3 -> S_n, where S_n denotes the symmetric group on n letters.

Original entry on oeis.org

1, 2, 10, 34, 146, 1036, 5692, 36380, 323164, 2394136, 19863416, 210278872, 1937685400
Offset: 1

Views

Author

Daniel McLaury, Apr 12 2017

Keywords

Crossrefs

A000085 gives the number of group homomorphisms S_2 -> S_n.

Programs

  • GAP
    List([1..8], n -> Length(AllHomomorphisms(SymmetricGroup(3), SymmetricGroup(n))));

Formula

a(n) = 6*A378279(n) + A000085(n). See A378163 for more information. - Jianing Song, Nov 27 2024

Extensions

a(8) from Georg Fischer, Jun 16 2022
a(9)-a(13) from Jianing Song, Nov 27 2024
Showing 1-4 of 4 results.