the 12 isometry classes of irreducible [12,4,5]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 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 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 1 0 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (3, 5)(4, 6)(8, 9)(10, 11), (2, 5)(4, 7)(8, 9)(10, 12) orbits: { 1 }, { 2, 5, 3 }, { 4, 6, 7 }, { 8, 9 }, { 10, 11, 12 } code no 2: ================ 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 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 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 1 0 0 0 0 0 0 0 0 1 , 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (3, 5)(4, 6)(10, 11), (1, 2)(8, 9) orbits: { 1, 2 }, { 3, 5 }, { 4, 6 }, { 7 }, { 8, 9 }, { 10, 11 }, { 12 } code no 3: ================ 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 , 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 , 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (3, 4)(8, 9), (1, 2)(8, 9), (1, 4, 2, 3)(6, 7)(11, 12) orbits: { 1, 2, 3, 4 }, { 5 }, { 6, 7 }, { 8, 9 }, { 10 }, { 11, 12 } code no 4: ================ 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 , 1 1 1 1 0 0 0 0 0 1 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 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 , 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 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 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (3, 4)(8, 9), (1, 10)(3, 4)(6, 12)(7, 11)(8, 9), (1, 6)(3, 9)(4, 8)(10, 12) orbits: { 1, 10, 6, 12 }, { 2 }, { 3, 4, 9, 8 }, { 5 }, { 7, 11 } code no 5: ================ 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 elements: ( 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 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 1 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 1 0 1 1 1 1 1 1 1 1 , 1 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 1 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 1 0 0 0 0 0 0 0 0 1 , 1 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 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 , 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (5, 6)(8, 9), (2, 3), (2, 6)(3, 5)(4, 7)(10, 12), (1, 7)(2, 8)(3, 9)(5, 6)(10, 11), (1, 10, 4, 11, 7, 12)(2, 6, 8)(3, 5, 9) orbits: { 1, 7, 12, 4, 11, 10 }, { 2, 3, 6, 8, 5, 9 } code no 6: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 the automorphism group has order 384 and is strongly generated by the following 7 elements: ( 1 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 1 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 1 0 0 1 1 0 1 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 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 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 , 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (7, 11), (6, 10), (4, 9), (3, 5)(4, 10)(6, 9), (2, 5, 3)(4, 10, 11, 9, 6, 7), (1, 5)(4, 8, 9, 12)(6, 10)(7, 11) orbits: { 1, 5, 3, 2 }, { 4, 9, 10, 7, 12, 6, 11, 8 } code no 7: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 elements: ( 1 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 1 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 1 0 1 1 1 0 1 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 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 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (7, 11), (6, 10), (4, 9), (3, 5)(4, 10)(6, 9), (2, 5, 3)(4, 10, 11, 9, 6, 7) orbits: { 1 }, { 2, 3, 5 }, { 4, 9, 10, 7, 6, 11 }, { 8, 12 } code no 8: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 6 elements: ( 1 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 1 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 1 0 1 0 0 1 1 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 , 1 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 1 0 0 0 0 0 0 0 0 1 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 1 , 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (7, 11), (6, 10), (3, 4)(7, 8, 11, 12), (2, 3)(6, 7)(10, 11), (2, 4)(6, 8, 10, 12) orbits: { 1 }, { 2, 3, 4 }, { 5 }, { 6, 10, 7, 12, 11, 8 }, { 9 } code no 9: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 1 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 1 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 1 0 0 1 0 1 0 1 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 , 1 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 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 1 0 0 0 0 0 0 0 0 1 , 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (7, 11), (3, 5)(4, 6)(9, 10), (1, 2)(3, 4)(5, 6)(7, 8, 11, 12) orbits: { 1, 2 }, { 3, 5, 4, 6 }, { 7, 11, 12, 8 }, { 9, 10 } code no 10: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 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 1 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 1 0 0 0 0 1 0 1 1 1 , 1 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 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 1 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 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 1 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (3, 5)(4, 6)(9, 10), (2, 3)(6, 7)(10, 11) orbits: { 1 }, { 2, 3, 5 }, { 4, 6, 7 }, { 8, 12 }, { 9, 10, 11 } code no 11: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 1 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 1 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 1 0 1 0 0 1 0 1 1 1 , 1 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 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 1 0 0 0 0 0 0 0 0 1 , 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 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 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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 , 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (8, 12), (3, 5)(4, 6)(9, 10), (1, 7)(2, 11)(4, 6)(9, 10), (1, 6)(2, 10)(4, 7)(9, 11), (1, 10)(2, 6)(4, 11)(7, 9) orbits: { 1, 7, 6, 10, 4, 9, 2, 11 }, { 3, 5 }, { 8, 12 } code no 12: ================ 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 , 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 1 0 0 1 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 , 1 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 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 , 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 9)(7, 10)(8, 11), (3, 9, 4)(6, 10, 7)(8, 11, 12), (2, 5)(3, 6)(4, 7)(9, 10), (2, 6)(3, 5)(4, 7)(8, 11)(9, 10), (2, 4, 3, 9)(5, 7, 6, 10)(8, 11) orbits: { 1 }, { 2, 5, 6, 9, 3, 10, 7, 4 }, { 8, 11, 12 }