CL-PERMUTATION can be downloaded with Quicklisp. Source code is here, which includes a README.
Example from the README:
(defparameter rubik-3x3
(group-from
'((3 5 8 2 7 1 4 6 33 34 35 12 13 14 15 16 9 10 11 20 21 22 23 24 17
18 19 28 29 30 31 32 25 26 27 36 37 38 39 40 41 42 43 44 45 46 47 48)
(17 2 3 20 5 22 7 8 11 13 16 10 15 9 12 14 41 18 19 44 21 46 23 24
25 26 27 28 29 30 31 32 33 34 6 36 4 38 39 1 40 42 43 37 45 35 47 48)
(1 2 3 4 5 25 28 30 9 10 8 12 7 14 15 6 19 21 24 18 23 17 20 22 43
26 27 42 29 41 31 32 33 34 35 36 37 38 39 40 11 13 16 44 45 46 47 48)
(1 2 38 4 36 6 7 33 9 10 11 12 13 14 15 16 17 18 3 20 5 22 23 8 27
29 32 26 31 25 28 30 48 34 35 45 37 43 39 40 41 42 19 44 21 46 47 24)
(14 12 9 4 5 6 7 8 46 10 11 47 13 48 15 16 17 18 19 20 21 22 23 24
25 26 1 28 2 30 31 3 35 37 40 34 39 33 36 38 41 42 43 44 45 32 29 27)
(1 2 3 4 5 6 7 8 9 10 11 12 13 22 23 24 17 18 19 20 21 30 31 32 25
26 27 28 29 38 39 40 33 34 35 36 37 14 15 16 43 45 48 42 47 41 44 46))))
PERM> (group-order rubik-3x3)
43252003274489856000