I'd recommend venting out the gable. Run a rigid vent from the gable wall to a point near your install, and use a 2' piece of flex duct to connect the fan to the rigid vent. The flex duct makes the bends easy (don't kink it) and allows the fan to be repaired from below in the future. For that length, I don't think you need to worry.

This could be an option, as long as a few conditions are met.

There should be a damper

A damper will prevent outside air from entering the exhaust pipe, traveling down the length and entering the conditioned space. Most exhaust vent covers are designed in such a way, so that even on windy days the exhaust can still be exhausted. If you just have a pipe pointing to the outside, it's possible the outside air pressure can overcome the exhaust air pressure preventing the exhaust from exhausting.

There shouldn't be a way for the exhaust to reenter the building

If you simply close the window on a pipe that does not completely fill the opening, it's very likely that air pressure differences will force the exhausted air right back in the window. You'll want to devise a way to prevent the exhausted air from reentering the building. This other answer illustrates a way to install the vent, while blocking the entire window opening.