GJ does not have functionality for implementing custom fields outside of making an entirely new plugin to do so.
Can you guide me to it?
No, we do not provide custom coding assistance here.
Does my subscription cover the option for you to integrate it?
No.
Can you provide templates for me to create it?
I recommend reviewing one of the existing GJ plugins that modifies GJs edit page with new fields.
What you're wanting is full field management for groups and that's not happening anytime soon nor would it be simple by any means to implement. This is something that will be added after CB 3.0 (long time from now) where we'll have all legacy APIs remove and replaced with newer APIs and our fields API rewritten to be usable outside of profiles.