0,4

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.

http://www-public.tu-bs.de:8080/~hubesche/number.html

Hans Ulrich Besche, Number of isomorphism types of finite groups of given order

a(0)=1 because 0!=1 and there is exactly one group of order one up to isomorphism

Sequence in context: A152015 A162256 A041719 this_sequence A025213 A116693 A154565

Adjacent sequences: A133774 A133775 A133776 this_sequence A133778 A133779 A133780

hard,nonn

Peter C. Heinig (algorithms(AT)gmx.de), Jan 02 2008