the 3 isometry classes of irreducible [9,2,6]_3 codes are: code no 1: ================ 1 1 1 1 1 1 1 2 0 2 2 1 1 1 0 0 0 2 the automorphism group has order 144 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 2 2 2 2 2 2 2 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 2 2 2 2 2 2 2 0 0 0 0 0 1 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 0 0 2 0 0 0 0 0 0 0 0 2 0 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 1 1 1 1 1 1 1 0 0 0 2 0 0 0 0 0 0 0 2 0 0 , 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 0 0 0 0 2 0 0 0 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 7), (6, 7, 8), (4, 5)(6, 8), (3, 6)(4, 8, 5, 7), (3, 8, 5, 7)(4, 6), (1, 2)(3, 8, 5, 6)(4, 7) orbits: { 1, 2 }, { 3, 6, 7, 8, 4, 5 }, { 9 } code no 2: ================ 1 1 1 1 1 0 0 2 0 1 1 1 0 0 1 1 0 2 the automorphism group has order 1296 and is strongly generated by the following 10 elements: ( 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 2 2 2 0 0 2 2 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 1 1 1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 , 1 1 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 2 2 2 0 0 2 2 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 9), (6, 7), (6, 9), (5, 8), (4, 8), (4, 5)(6, 7), (4, 7, 5, 6)(8, 9), (2, 3)(4, 8, 5), (1, 8)(2, 5, 3, 4)(6, 7), (1, 8, 6, 2, 4, 7, 3, 5, 9) orbits: { 1, 8, 9, 5, 4, 7, 6, 2, 3 } code no 3: ================ 1 1 1 1 1 0 0 2 0 2 2 1 1 0 1 1 0 2 the automorphism group has order 288 and is strongly generated by the following 7 elements: ( 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 1 1 0 1 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 2 2 1 1 0 1 1 0 0 0 0 0 2 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 1 1 1 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 0 0 0 0 2 0 0 1 1 1 1 1 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (7, 9), (6, 7), (6, 7, 9), (5, 8), (3, 8)(4, 5)(6, 7), (3, 5)(4, 8)(6, 7), (1, 3, 5)(2, 4, 8) orbits: { 1, 5, 8, 4, 3, 2 }, { 6, 7, 9 }