  We construct a connected finite loop space of rank 66 and dimension 1254
whose rational cohomology is not isomorphic as a graded vector space to the
rational cohomology of any compact Lie group, hence providing a counterexample
to a classical conjecture. Aided by machine calculation we verify that our
counterexample is minimal, i.e., that any finite loop space of rank less than
66 is in fact rationally equivalent to a compact Lie group, extending the
classical known bound of 5.
