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%I A133777
%S A133777 1,1,1,2,15,47,840
%N A133777 Number of isomorphism types of groups of order n!.
%C A133777 This sequence is interesting in view of Cayley's theorem which says that 
               every finite group with n elements is isomorphic to a subgroup of 
               the symmetric group S_n whose number of elements is n!. Therefore 
               a(n) - 1 gives the number of groups "competing" with S_n in this 
               respect. The eighth term, a(7), i.e. the number of isomorphism types 
               of groups of order 7!=5040, seems to be unknown.
%D A133777 http://www-public.tu-bs.de:8080/~hubesche/number.html
%H A133777 Hans Ulrich Besche, <a href="http://www-public.tu-bs.de:8080/~hubesche/
               number.html">Number of isomorphism types of finite groups of given 
               order</a>
%e A133777 a(0)=1 because 0!=1 and there is exactly one group of order one up to 
               isomorphism
%Y A133777 Sequence in context: A152015 A162256 A041719 this_sequence A025213 A116693 
               A154565
%Y A133777 Adjacent sequences: A133774 A133775 A133776 this_sequence A133778 A133779 
               A133780
%K A133777 hard,nonn
%O A133777 0,4
%A A133777 Peter C. Heinig (algorithms(AT)gmx.de), Jan 02 2008

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