Your online store provides tools to rename any existing attribute group, change the groups sorting on the page and delete a group if required.
Here's how you can do this:
On the Classes & Attributes page of your store's Admin area (Catalog > Classes & Attributes), locate the groups of attributes you want to edit.
Global Attributes - Catalog > Classes & Attributes > All Attributes
Product Class Attributes - Catalog > Classes & Attributes > Product Classes
NOTE: With the product class attributes, you need one additional step to access the attributes listing page - click the Edit attributes (N) link opposite a particular product class.
Click the "Manage groups" button.
A popup titled "Manage attribute groups" appears.
Use the tools of the "Manage attribute groups" popup for editing:
To rename a group, click on its name. The group name field will become editable.
To change the order of the attribute groups on the list, drag and drop the items to their new positions.
To delete a group, click the Trash icon opposite it.
NOTE: Deleting a group does not delete the attributes it has. Instead, after you delete a group, its contents will relocate to other attributes having no associated groups.
When the attribute group editing is complete, click "Save changes."