A104453 Smallest order for which there are n nonisomorphic finite Hamiltonian groups, or 0 if no such order exists.

8, 72, 216, 1800, 648, 5400, 1944, 88200, 27000, 16200, 10, 5832, 264600, 0, 48600, 17496, 10672200, 0, 1323000, 0, 793800, 20, 243000, 52488, 0, 32016600, 405000, 0, 9261000, 2381400, 0, 157464

Offset: 1

Author

Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), Tomaz Pisanski, Apr 19 2005

Keywords

• nonn
• hard

References

• R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, New York, Dover, 1956.
• J. C. Lennox and S. E. Stonehewer, Subnormal Subgroups of Groups, Oxford University Press, 1987.

Links

• B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups, arXiv:math/0503183 [math.CO], 2005.
• T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989), 157-167.
• Eric Weisstein's World of Mathematics, Abelian Group
• Eric Weisstein's World of Mathematics, Hamiltonian Group

Crossrefs

Cf. A000688, A063966, A104488, A104407, A104404, A104452.

Formula

S_h(n) denotes the smallest number k for which exactly n nonisomorphic hamiltonian groups of order k exist. Here 0 indicates the case when n is not a product of partition numbers and S_h(n) does not exist.