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A070733
Size of largest conjugacy class in A_n, the alternating group on n symbols.
2
1, 1, 1, 4, 20, 90, 630, 3360, 30240, 226800, 2494800, 23950080, 311351040, 3632428800, 54486432000, 747242496000, 12703122432000, 200074178304000, 3801409387776000, 67580611338240000, 1419192838103040000, 28100018194440192000, 646300418472124416000
OFFSET
1,4
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
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002
EXTENSIONS
More terms from Eric M. Schmidt, Sep 13 2014
STATUS
approved