You don't want to go straight up out the roof. On cold days the condensation will drip back down the duct work and into the fan and made a nasty mess. Best is to go straight outside to an exterior wall. Install the fan as close to the exterior wall as possible. I know Ask This Old House has an episode on how to install one. They do things the right way and real professional.
A window just doesn’t cut the cheese when it comes to properly evacuating the stank...