Dan Hoey writes in his e-mail message of 1994/11/08
The way I view this is as follows. The entire cube group C is a
permutation group group on 6*9 points, generated by the six face
turns U, D, L, R, F, B; the three middle slice turns M_U, M_L,
M_F; and the reflection S. This group has a subgroup M of
symmetries of the cube (of order 48), generated by U M_U D',
L M_L R', F M_F B', and S. Another subgroup is G, generated by
the six face turns, which has index 48 in G. G is a normal
divisor of C, G is the semidirect product of M and G. The same is
true for GE and GC.
I think two of those G's are supposed to be C's, right?
Correct (wouldn't make any sense for a group G to be a subgroup in itself
of index 48 ;-).
Dan Hoey continues
As for when I wroteM class Edge Corner Corner times edge (class size) F.P. F.P. / (96*class size) ^^^^^^^^^^^^^^^^^^^^^^
That's not a typo. I was just saying that column 4 is equal to column
2 times column 3, divided by column 1, divided by 96. Perhaps I
should have factored column 1 out of columns 2 and 3 first to avoid
Again you are correct. But it was confusing, at least to me.
Have a nice day.
-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany