The 'delete group' functionality appears not to do anything.
Expect results: Performing a 'delete group' operation would cause the deleted group to no longer be included in the list of groups visible in the relevant account's management page.
Actual results: Clicking the 'Delete group' button in my account's list of groups results in a confirmation dialog asking me whether I am sure I want to delete the group. This dialog contains an OK button. Clicking this OK button dismisses the dialog, thus revealing the list of groups again, which is unchanged.
Forcing a refresh of the groups list, by visiting a different management page then returning to the groups list, results in display of the same list of groups, still containing the supposedly-deleted group.
Logging out and logging back in, then viewing the list of groups again, results in display of the same groups list, still including the supposedly-deleted group.
There appears to be no way to cause a group to no longer be included in this list.