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A174511
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The number of isomorphism classes of subgroups of the symmetric group S_n.
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2
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1, 2, 4, 9, 16, 29, 55, 137, 241, 453, 894, 2065, 3845
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OFFSET
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1,2
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COMMENTS
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Two subgroups are considered to be isomorphic here if they are isomorphic as abstract groups, not as permutation groups. - N. J. A. Sloane, Nov 28 2010
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LINKS
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Table of n, a(n) for n=1..13.
A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023, 2013. - From N. J. A. Sloane, Feb 19 2013
J. Schmidt, Enumerating all subgroups of the symmetric group.
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EXAMPLE
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a(3) = 4 since S_3 contains up to isomorphism exactly one subgroup of each of the orders 1,2,3,6.
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PROG
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(GAP)
a:=[];
for n in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] do
G:=SymmetricGroup(n);
R:=ConjugacyClassesSubgroups(G);
RR:=ListX(R, Representative);
T:=[RR[1]];
for g in RR do
flag:=false;
for h in T do
if IsomorphismGroups(g, h)<>fail then
flag:=true;
break;
fi;
od;
if flag=false then Add(T, g); fi;
od;
Add(a, Size(T));
od;
Print(a, "\n");
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CROSSREFS
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Cf. A000638, A005432.
Sequence in context: A000291 A081055 A034446 * A034452 A034449 A082894
Adjacent sequences: A174508 A174509 A174510 * A174512 A174513 A174514
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KEYWORD
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nonn,more
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AUTHOR
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W. Edwin Clark, Nov 28 2010
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EXTENSIONS
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a(11) and a(12) from Stephen A. Silver, Feb 24 2013
a(13) (as calculated by Jack Schmidt) from L. Edson Jeffery, May 26 2013
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STATUS
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approved
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