I think it would be extremely helpful to have editable descriptions of what a user group has permission to do. This would be for cases where new admins or users that can assign user groups can quickly understand what a given group has access to.
This would not be auto-generated, but rather an additional optional field in the user group settings page.
I think having a line similar to a field's instructions text, or as a tooltip next to the name would both be fine and not clutter the interface too much.
+1. Would be great to be able to tell the users, and remind myself, what specific user groups are set up for.
Just added this for 3.5!

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Just added this for 3.5!