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A174511 The number of isomorphism classes of subgroups of the symmetric group S_n. 2


%S 1,2,4,9,16,29,55,137,241,453,894,2065,3845

%N The number of isomorphism classes of subgroups of the symmetric group S_n.

%C 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

%H A. Distler and T. Kelsey, <a href="http://arxiv.org/abs/1301.6023">The semigroups of order 9 and their automorphism groups</a>, arXiv preprint arXiv:1301.6023, 2013. - From _N. J. A. Sloane_, Feb 19 2013

%H J. Schmidt, <a href="http://math.stackexchange.com/questions/76176/enumerating-all-subgroups-of-the-symmetric-group">Enumerating all subgroups of the symmetric group.</a>

%e a(3) = 4 since S_3 contains up to isomorphism exactly one subgroup of each of the orders 1,2,3,6.

%o (GAP)

%o a:=[];

%o for n in [1,2,3,4,5,6,7,8,9,10] do

%o G:=SymmetricGroup(n);

%o R:=ConjugacyClassesSubgroups(G);

%o RR:=ListX(R,Representative);

%o T:=[RR[1]];

%o for g in RR do

%o flag:=false;

%o for h in T do

%o if IsomorphismGroups(g,h)<>fail then

%o flag:=true;

%o break;

%o fi;

%o od;

%o if flag=false then Add(T,g); fi;

%o od;

%o Add(a,Size(T));

%o od;

%o Print(a,"\n");

%Y Cf. A000638, A005432.

%K nonn,more

%O 1,2

%A _W. Edwin Clark_, Nov 28 2010

%E a(11) and a(12) from _Stephen A. Silver_, Feb 24 2013

%E a(13) (as calculated by Jack Schmidt) from _L. Edson Jeffery_, May 26 2013

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)