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A277566 Irregular table by rows: Orders of subgroups of the symmetric group S_n. 2
1, 1, 2, 1, 2, 3, 6, 1, 2, 3, 4, 6, 8, 12, 24, 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 36, 40, 42, 48, 60, 72, 120, 144, 168, 240, 360, 720, 2520, 5040, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 30, 32, 36, 40, 42, 48, 56, 60, 64, 72, 96, 120, 128, 144, 168, 180, 192, 240, 288, 336, 360, 384, 576, 720, 1152, 1344, 1440, 2520, 5040, 20160, 40320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself).

LINKS

Charles R Greathouse IV, Rows n = 1..12 of table, flattened

Götz Pfeiffer, Numbers of subgroups of various families of groups

EXAMPLE

1;

1, 2;

1, 2, 3, 6;

1, 2, 3, 4, 6, 8, 12, 24;

1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120;

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 36, 40, 42, 48, 60, 72, 120, 144, 168, 240, 360, 720, 2520, 5040;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 30, 32, 36, 40, 42, 48, 56, 60, 64, 72, 96, 120, 128, 144, 168, 180, 192, 240, 288, 336, 360, 384, 576, 720, 1152, 1344, 1440, 2520, 5040, 20160, 40320;

PROG

(GAP) LoadPackage("sonata");

a := function(n)

  return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size)));

end;; # Charles R Greathouse IV, Nov 28 2016

CROSSREFS

Row lengths are given by A218913.

See A243748 for a closely related sequence.

Sequence in context: A135938 A079210 A070861 * A261144 A106524 A323641

Adjacent sequences:  A277563 A277564 A277565 * A277567 A277568 A277569

KEYWORD

nonn,tabf

AUTHOR

Charles R Greathouse IV, Nov 28 2016

STATUS

approved

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Last modified January 21 10:25 EST 2022. Contains 350477 sequences. (Running on oeis4.)