(With this layout, it would likely be best to have separate matrices for user groups and users.)
Group names can be changed on the fly (notice that they're all in fields)?
I didn't add it in, but a "Quick check all" ability for rows as well?
Alternatively, set it up so that e.g. if I double clicked the Allow value for Edit profile: under the Members group, every other group's setting for Edit profile: would be changed to Allow as well.
I didn't add it in, but maybe each group could have a gripper at one of the corners, allowing for their order to be changed?
I didn't add it in, but have the buttons Update Permissions, Revert to Previous, and Revert to Default at the bottom of each individual group?
To the bottom right of all of the groups, have the same buttons, except that they affect all groups?
I didn't add this in either, but have a button to create a new group to the top right of the existing groups (a simple + button, maybe)? Clicking it would result in a new group appearing to the right of the rest, with its name input field selected.
Edit: Nearly forgot about how to delete groups! Random ideas:
Blanking out a group's name and then deselecting its name input field results in a warning appearing above the field, stating that the group will be deleted when the user applies changes to either the blanked-out group or all groups (unless they type a name back in)?
A simple Delete Group button next to the rest of the buttons at the bottom of each group?