I received this e-mail from DeviantArt's help-desk after submitting a complaint about not being able to move or remove deviations, and figured I should share it with you to save some hassle! You've all experienced it by now, and many of you have already figured it out, or been told how to do it. I'm quoting the reply with DA's own links, you can check them yourselves, the ones used are only fave.me, the official DA short-URL, various deviantart.com links, and to deviantart.zendesk.com, the official DeviantArt help-desk site.
Update: Probably after getting massive complaints from group owners, DA has now added an "Edit Page" button on gallery