It depends. Ordinarily, the showing of a film by a group or club is for entertainment purposes and thus PPR is required. However, if the group's purpose and activities are ordinarily educational in nature and the showing of the film is in furtherance of those educational purposes and activities, then it may be fair use to show the film without PPR.
There are some cases in where the distributor of the documentary will allow for educational screening. For example, let say there is a documentary on Netflix that you want to show for your student club or in-class, you can see if the documentary has the "GRANT OF PERMISSION FOR EDUCATIONAL SCREENINGS" section as seen below:
Obtaining Public Performance Rights
To obtain PPR, you must get licensing for the film through by either contacting the copyright holder or contacting the licensing service representing the particular studio or title .PPR is mostly sought out by organizations or institutions, which may be difficult for individuals to obtain.
Do seek out other alternative, try finding films that are available through Kanopy or the public domain.