A070733 Size of largest conjugacy class in A_n, the alternating group on n symbols.

1, 1, 1, 4, 20, 90, 630, 3360, 30240, 226800, 2494800, 23950080, 311351040, 3632428800, 54486432000, 747242496000, 12703122432000, 200074178304000, 3801409387776000, 67580611338240000, 1419192838103040000, 28100018194440192000, 646300418472124416000

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002

Keywords

• nonn

Comments

For n > 5, the largest conjugacy class in A_n corresponds to the cycle type (n-2, 2) if n is even, (n-3, 2, 1) if n is odd. - Eric M. Schmidt, Sep 13 2014

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A059171, A001710, A000702, A029726.

Programs

GAP

a:=function(n)
local G,CC,SCC,SCC1;
G:=AlternatingGroup(n);
CC:=ConjugacyClasses(G);;
SCC:=List(CC,Size);
return Maximum(SCC);
end;;  #  W. Edwin Clark, Feb 02 2014

Mathematica

a[n_] := (n!/2) / If[OddQ[n],  n-3, n-2]; a[1] = a[2] = a[3] = 1; a[4] = 4; a[5] = 20; Array[a, 20] (* Amiram Eldar, Jul 12 2025 *)

PARI

a(n) = if(n < 6, [1, 1, 1, 4, 20][n], (n!/2) / if(n % 2,  n-3, n-2)); \\ Amiram Eldar, Jul 12 2025

Formula

For n > 5, a(n) = n!/(2(n-2)) if n is even, a(n) = n!/(2(n-3)) if n is odd. - Eric M. Schmidt, Sep 13 2014

Sum_{n>=1} 1/a(n) = 111/10 + 1/e - 3*e. - Amiram Eldar, Jul 12 2025

Extensions

More terms from Eric M. Schmidt, Sep 13 2014