Notes on the various Super-Groups --------------------------------- I have calculated the size of the super-groups for various subgroups of the cube. I have suffixed the standard group names with the letter c to show that the centre orientations are significant. The groups are (ranked smallest to largest): Size (slice) = 768 Size (slicec) = 24,576 Size (slicec) / Size (slice) = 32 The following reference confirms this calculation and expounds further on the nature of the slice group... The Slice Group in Rubik's Cube, by David Hecker, Ranan Banerji Mathematics Magazine, Vol. 58 No. 4 Sept 1985 Size (antisl) = 6,144 Size (antislc) = 49,152 Size (antislc) / Size (antisl) = 8 Size (sq) = 663,552 Size (sqc) = 5,308,416 Size (sqc) / Size (sq) = 8 Size (ur) = 73,483,200 Size (urc) = 587,865,600 Size (urc) / Size (ur) = 8 Size (domino) = 406,425,600 Size (dominoc)= 3,251,404,800 Size (dominoc) / Size (domino) = 8 Size (cube) = 43,252,003,274,489,856,000 Size (cubec) = 88,580,102,706,155,225,088,000 Size (cubec) / Size (cube) = 2,048 The case of the super squares group (sqc) is interesting. It is only possible to rotate opposite centres 180 degrees. There are actually 8 centres in the super square's group: (1 way) Identity (1 way) All 6 centres rotated 180 degrees (3 ways) 2 opposite centres rotated 180 degrees (3 ways) 2 pairs of opposite centres rotated 180 degrees