Player Groups are the precursor to Player Minor Factions, which allow you to request the creation of an Elite Dangerous in-game faction related to your Player Group or Squadron.
Once you've filled out this form, you will be eligible to request a Player Minor Faction here:
https://tools.elitedangerous.com/en/factions You will not receive confirmation of your Player Group registration. The details in this form will be used to validate your Player Group for the use in the Player Minor Faction application form.