From:

~~~ Subject:

Dan Hoey writes in his e-mail message of 1994/11/08

Martin.Schoenert@math.rwth-aachen.de writes:

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 wrote

M 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

this confusion.

Again you are correct. But it was confusing, at least to me.

Have a nice day.

Martin.

-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany