Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra = $10^9$ and Prandtl number $\sigma$ = 6.4. In this Letter we discuss two topics: the breakdown under rotation of the domain-filling large-scale circulation (LSC) typical for confined convection, and the convective heat transfer through the fluid layer, expressed by the Nusselt number. The presence of the LSC is addressed for several rotation rates. For Rossby numbers Ro $\leq 1.2$ no LSC is found (the Rossby number indicates relative importance of buoyancy over rotation, hence small Ro indicates strong rotation). For larger Rossby numbers a precession of the LSC in anticyclonic direction (counter to the background rotation) is observed. It is shown that the heat transfer has a maximal value close to Ro = 0.18 being about 15% larger than in the non-rotating case Ro = $\infty.$ Since the LSC is no longer present at this Rossby value we conclude that the peak heat transfer is independent of the LSC.