It was my understanding that the size (number of possible positions) of
the supergroup was only (4^6)/2 times as large as the normal group, i.e.,
that there was another level of parity involved. This would imply that
you can rotate a center facie 180 degrees, but not 90 (at least, not without
changing something else). I'd be most interested in seeing one of your
"many apparently 'null operations'" that rotates one center face 90 degrees.