the 7 isometry classes of irreducible [13,3,8]_3 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 2 0 0 2 2 2 1 1 1 1 0 0 0 0 2 0 2 1 0 2 2 1 0 1 1 0 0 0 2 the automorphism group has order 48 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 2 2 2 2 2 2 , 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 2 2 2 2 2 2 , 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 2 0 1 1 2 0 2 2 0 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 0 0 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 0 0 0 2 0 0 0 0 0 1 0 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 0 2 0 0 0 0 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 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 , 1 0 0 0 0 0 0 0 0 0 2 1 0 2 2 1 0 1 1 0 0 2 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 2 2 2 1 1 1 1 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 0 0 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (10, 11), (8, 9), (4, 5)(10, 11), (3, 13)(4, 10, 5, 11)(6, 12)(8, 9), (2, 3)(6, 7)(8, 10, 9, 11), (2, 3, 13)(4, 8, 11)(5, 9, 10)(6, 12, 7) orbits: { 1 }, { 2, 3, 13 }, { 4, 5, 11, 10, 9, 8 }, { 6, 12, 7 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 2 0 0 2 2 2 1 1 1 1 0 0 0 0 2 0 2 2 0 2 2 1 0 1 1 0 0 0 2 the automorphism group has order 64 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 2 2 2 2 2 2 , 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 0 1 1 2 0 2 2 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 0 0 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 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 , 0 2 0 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 0 0 0 0 0 0 2 0 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 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 0 2 0 0 1 1 1 1 1 1 1 1 1 1 , 0 0 0 0 0 0 0 0 2 0 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 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (10, 11), (8, 9), (4, 5)(8, 9), (3, 13)(4, 11, 5, 10)(6, 12)(8, 9), (1, 2)(4, 5)(8, 9)(10, 11), (1, 9)(2, 8)(3, 6)(4, 10)(5, 11)(12, 13) orbits: { 1, 2, 9, 8 }, { 3, 13, 6, 12 }, { 4, 5, 10, 11 }, { 7 } code no 3: ================ 1 1 1 1 1 1 1 1 1 1 2 0 0 2 2 2 1 1 1 1 0 0 0 0 2 0 2 1 0 2 1 1 0 2 1 0 0 0 2 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 1 1 1 1 1 1 1 , 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 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 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 1 1 1 1 1 1 1 , 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 2 2 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (10, 11), (5, 6)(10, 11), (2, 3)(4, 8)(5, 11, 6, 10)(7, 9), (2, 4)(3, 8)(7, 9)(10, 11)(12, 13) orbits: { 1 }, { 2, 3, 4, 8 }, { 5, 6, 10, 11 }, { 7, 9 }, { 12, 13 } code no 4: ================ 1 1 1 1 1 1 1 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 0 2 0 2 1 2 1 0 1 0 1 0 1 0 0 2 the automorphism group has order 48 and is strongly generated by the following 6 elements: ( 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 1 2 1 0 1 0 1 0 1 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 1 , 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 1 1 1 1 1 0 0 0 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 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 0 0 2 0 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 0 0 0 0 0 0 2 0 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 0 0 0 0 0 2 0 0 2 1 2 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 2 0 , 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 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 0 0 0 0 0 2 , 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 1 2 1 0 1 0 1 0 1 0 0 0 0 2 0 0 0 0 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (10, 13), (9, 12), (7, 11), (2, 3)(5, 6)(9, 10, 12, 13), (1, 2)(6, 8)(7, 9, 11, 12), (1, 3)(5, 8)(7, 10, 11, 13)(9, 12) orbits: { 1, 2, 3 }, { 4 }, { 5, 6, 8 }, { 7, 11, 12, 13, 9, 10 } code no 5: ================ 1 1 1 1 1 1 1 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 0 2 0 2 1 2 2 0 1 0 1 0 1 0 0 2 the automorphism group has order 128 and is strongly generated by the following 7 elements: ( 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 1 2 2 0 1 0 1 0 1 , 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 , 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 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 0 0 0 0 0 2 , 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 2 1 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 2 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (10, 13), (9, 12), (7, 11)(9, 12), (3, 4)(7, 11), (2, 8)(3, 9, 4, 12)(7, 13, 11, 10), (1, 2)(6, 8)(7, 9, 11, 12), (1, 6)(2, 8)(3, 13)(4, 10)(7, 9, 11, 12) orbits: { 1, 2, 6, 8 }, { 3, 4, 12, 13, 9, 10, 11, 7 }, { 5 } code no 6: ================ 1 1 1 1 1 1 1 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 0 2 0 0 0 2 1 0 2 1 2 1 1 0 0 2 the automorphism group has order 288 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 2 0 1 2 1 2 2 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 1 , 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 , 0 0 2 1 0 2 1 2 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (10, 13), (6, 8)(7, 9)(11, 12), (4, 5)(6, 11)(8, 12), (3, 6, 12)(4, 11, 9)(5, 7, 8), (3, 4, 5)(6, 11, 7)(8, 12, 9), (1, 2)(3, 4)(6, 7)(8, 9), (1, 13)(2, 10)(3, 9, 8, 4)(5, 7, 12, 6) orbits: { 1, 2, 13, 10 }, { 3, 12, 5, 4, 11, 8, 6, 7, 9 } code no 7: ================ 1 1 1 1 1 1 1 0 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 0 2 0 1 0 2 1 0 2 1 2 1 1 0 0 2 the automorphism group has order 72 and is strongly generated by the following 6 elements: ( 2 0 0 0 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 0 0 0 2 0 0 0 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 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 1 0 2 1 0 2 1 2 1 1 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 1 1 1 0 0 1 1 0 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 1 0 0 0 0 2 2 2 2 2 2 2 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 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 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 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 2 , 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 1 1 1 0 0 1 1 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 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (10, 13), (4, 5)(6, 12)(7, 9)(8, 11), (3, 8)(4, 9)(5, 12)(6, 7), (3, 12)(4, 8)(5, 9)(7, 11), (3, 11)(4, 6)(5, 7)(9, 12), (1, 2)(3, 5, 4)(6, 8, 11, 12, 7, 9) orbits: { 1, 2 }, { 3, 8, 12, 11, 4, 6, 5, 9, 7 }, { 10, 13 }