the 1 isometry classes of irreducible [6,1,6]_3 codes are: code no 1: ================ 1 1 1 1 1 2 the automorphism group has order 720 and is strongly generated by the following 10 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 2 2 2 2 2 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 , 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 , 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 0 , 2 0 0 0 0 0 2 0 0 0 1 1 1 1 1 0 0 0 2 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 , 1 0 0 0 0 2 2 2 2 2 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 , 0 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 0 0 , 0 2 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 , 2 2 2 2 2 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (4, 5), (3, 5), (3, 5, 4), (3, 6), (2, 5)(3, 4), (2, 6)(3, 5), (1, 5)(3, 4), (1, 3, 2)(4, 5), (1, 5, 3, 4, 2, 6) orbits: { 1, 5, 2, 6, 4, 3 }