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
-
A378279 := function(n)
local S;
S := SymmetricGroup(n);
return Sum(IsomorphicSubgroups(S, SymmetricGroup(3)), x->Index(S, Normalizer(S, Image(x))));
end;
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
-
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
-
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
A000085 gives the number of group homomorphisms S_2 -> S_n.
Showing 1-4 of 4 results.