How to structure MySQL database tables for users and how to handle adding/removing permissions?

I am making a database structure for users, who can become part of a group, and within that group the admin of the group can assign as many permissions to a user as they would like.
This part seems easy. I have 4 tables:

 USERS           GROUPS             PERMISSIONS      PERMISSIONS_GROUPS -------  ---------------------    --------------    ------------------- | UID |  | GID | UID(creator) |   | PID | NAME |    | UID | GID | PID | 

I think this is the best way to handle this. I have a few questions about how to handle permissions for the creator of the group, and how to handle permissions if I were to delete a permission or add a permission.
For instance, when a user makes a group. Do I query all of the permissions and in a while loop insert a PERMISSIONS_GROUPS record for every row in the permissions table? If I add a new permission, do I have to query every UID from the GROUPS table and run a while loop to insert the new permission into PERMISSIONS_GROUPS? I just want to make sure I am not missing something simple here. For structure/scripting I am using MySQL and PHP.