A070733 - OEIS

%I #13 Apr 20 2024 23:50:44

%S 1,1,1,4,20,90,630,3360,30240,226800,2494800,23950080,311351040,

%T 3632428800,54486432000,747242496000,12703122432000,200074178304000,

%U 3801409387776000,67580611338240000,1419192838103040000,28100018194440192000,646300418472124416000

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

%C 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

%H Eric M. Schmidt, <a href="/A070733/b070733.txt">Table of n, a(n) for n = 1..100</a>

%F 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

%o (GAP)

%o a:=function(n)

%o local G,CC,SCC,SCC1;

%o G:=AlternatingGroup(n);

%o CC:=ConjugacyClasses(G);;

%o SCC:=List(CC,Size);

%o return Maximum(SCC);

%o end;;  #  _W. Edwin Clark_, Feb 02 2014

%Y Cf. A059171, A001710, A000702, A029726.

%K nonn

%O 1,4

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

%E More terms from _Eric M. Schmidt_, Sep 13 2014