Clock optimal solver

As there're only 18 possible moves in WCA notation (instead of all 30 moves of the clock puzzle), we can easily solve the clock by brute-force search + Gaussian Elimination.
The average solution length of the optimal solver is about 10.8 moves, which is 2 moves less than randomly generated moves (14 * (1 - 1/12) = 12.83). 
I see. I like the idea of generating all of them just to have the generation code in here. Right now those magic numbers are scary. How much code are we talking about? How long would initialization take? How big would the table be?