Q:

Max order for which connected Cayley Graphs are known to be Hamiltonian

There is a well-known conjecture that all connected Cayley graphs are Hamiltonian.
For how large a value of n has the conjecture been verified (i.e., for all groups whose order is at most n)?

A:

According to :
http://arxiv.org/pdf/1009.5795v3.pdf 
this is known for all n up to 120 except 72, 96, 108 and 120.

