the 24 isometry classes of irreducible [20,14,4]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 184320 and is strongly generated by the following 13 elements: ( 1 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 1 0 1 0 1 0 0 1 , 1 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 1 0 1 1 0 0 0 1 , 1 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 1 0 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 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 , 1 0 1 0 1 0 0 1 1 0 1 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 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 16)(7, 19)(15, 17)(18, 20), (6, 15)(7, 20)(16, 17)(18, 19), (6, 7)(15, 20)(16, 19)(17, 18), (5, 15)(6, 12)(13, 17)(14, 16), (5, 16)(6, 13)(12, 17)(14, 15), (5, 13)(6, 16)(12, 14)(15, 17), (4, 9)(5, 12)(10, 11)(13, 14), (4, 10)(5, 13)(9, 11)(12, 14), (4, 16, 11, 15)(5, 14)(6, 9, 17, 10)(12, 13), (3, 8)(4, 6, 5, 9, 15, 12)(10, 17, 13)(11, 16, 14)(18, 19), (2, 3)(6, 17)(7, 18)(9, 10)(12, 13), (1, 13)(2, 14)(3, 5)(8, 12), (1, 16, 18, 2, 6, 19, 8, 15, 7, 3, 17, 20)(4, 9, 11, 10)(5, 14) orbits: { 1, 13, 20, 17, 6, 5, 14, 12, 18, 7, 15, 16, 9, 10, 3, 4, 2, 8, 19, 11 } code no 2: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 36864 and is strongly generated by the following 10 elements: ( 1 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 1 0 0 1 1 0 0 1 , 1 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 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 , 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 , 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 20)(18, 19), (6, 18)(19, 20), (5, 15)(11, 14)(12, 17)(13, 16), (5, 17)(11, 16)(12, 15)(13, 14), (5, 11)(12, 13)(14, 15)(16, 17), (4, 16)(8, 17)(9, 14)(10, 15), (4, 13, 17)(5, 14, 10)(8, 12, 16)(9, 11, 15), (3, 7)(4, 11, 8, 5)(6, 18)(9, 12, 10, 13)(14, 15), (2, 7)(4, 15, 9, 17)(6, 19)(8, 16, 10, 14)(11, 13), (1, 15, 12, 2, 14, 13)(3, 17, 5, 7, 16, 11)(4, 8)(9, 10) orbits: { 1, 13, 16, 14, 12, 4, 10, 11, 17, 8, 7, 15, 9, 5, 2, 3 }, { 6, 20, 18, 19 } code no 3: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 3072 and is strongly generated by the following 10 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 , 1 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 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 , 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 , 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 12)(11, 13)(14, 16)(15, 17), (5, 16)(11, 17)(12, 14)(13, 15), (5, 15)(11, 14)(12, 17)(13, 16), (3, 7)(4, 8)(6, 18)(12, 13)(14, 15), (3, 8)(4, 7)(5, 17)(6, 18)(11, 16)(19, 20), (2, 7)(4, 9)(5, 14, 12, 16)(6, 19)(11, 17, 13, 15), (2, 7, 3)(4, 8, 9)(5, 16, 12, 17, 11, 15)(6, 18, 19)(13, 14), (2, 9)(3, 7, 8, 4)(5, 17)(6, 19, 18, 20)(12, 14, 15, 13), (1, 9)(2, 10)(3, 8)(4, 7)(5, 13, 11, 12)(6, 18)(14, 16, 15, 17), (1, 12, 4, 17)(2, 13, 8, 16)(3, 11, 9, 14)(5, 10, 15, 7)(6, 18) orbits: { 1, 9, 17, 4, 8, 2, 11, 15, 12, 5, 7, 3, 13, 10, 16, 14 }, { 6, 18, 19, 20 } code no 4: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 , 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 11)(6, 17)(9, 10)(12, 13)(18, 19), (4, 10)(5, 13)(6, 19)(8, 9)(11, 12)(17, 18), (3, 7)(4, 9, 8, 10)(5, 13, 11, 12)(6, 18, 17, 19)(14, 15), (2, 7)(4, 9)(6, 18)(11, 13)(14, 16), (1, 7)(2, 3)(4, 10)(8, 9), (1, 8)(2, 9)(3, 10)(4, 7)(6, 18)(11, 13)(14, 16) orbits: { 1, 7, 8, 3, 2, 4, 9, 10 }, { 5, 11, 13, 12 }, { 6, 17, 19, 18 }, { 14, 15, 16 }, { 20 } code no 5: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 120 and is strongly generated by the following 8 elements: ( 1 0 0 0 0 0 0 1 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 0 0 1 , 1 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 0 0 1 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 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 , 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(8, 11)(9, 12)(10, 13)(19, 20), (3, 4)(7, 8)(12, 14)(13, 15)(18, 19), (3, 5)(7, 11)(9, 14)(10, 15)(18, 20), (2, 3)(8, 9)(11, 12)(15, 16)(17, 18), (2, 4)(7, 9)(11, 14)(13, 16)(17, 19), (1, 4)(6, 19)(7, 10)(11, 15)(12, 16), (1, 2)(6, 17)(9, 10)(12, 13)(14, 15), (1, 5)(2, 4)(6, 20)(7, 16)(8, 15)(9, 13)(11, 14)(17, 19) orbits: { 1, 4, 2, 5, 3 }, { 6, 19, 17, 20, 18 }, { 7, 8, 11, 9, 10, 16, 15, 12, 14, 13 } code no 6: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 1536 and is strongly generated by the following 9 elements: ( 1 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 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 , 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 16)(17, 18)(19, 20), (5, 11)(12, 13)(14, 15), (5, 16)(6, 11)(12, 18)(13, 17)(14, 20)(15, 19), (4, 10)(5, 13)(6, 18)(8, 9)(11, 12)(16, 17), (4, 9)(5, 12)(6, 17)(8, 10)(11, 13)(16, 18), (3, 7)(4, 8)(6, 16)(12, 13)(14, 15), (3, 8, 10)(4, 9, 7)(5, 14, 12, 11, 15, 13)(6, 20, 17)(16, 19, 18), (1, 8, 2, 4)(3, 9, 7, 10)(6, 16)(12, 13)(14, 15), (1, 9)(2, 10)(3, 4)(7, 8) orbits: { 1, 4, 9, 10, 8, 7, 2, 3 }, { 5, 11, 16, 13, 12, 6, 17, 18, 15, 14, 20, 19 } code no 7: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 256 and is strongly generated by the following 7 elements: ( 1 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 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 , 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 17)(16, 18)(19, 20), (5, 11)(12, 13)(14, 15), (4, 10)(5, 12)(6, 18)(8, 9)(11, 13)(14, 15)(16, 17), (4, 9)(5, 13)(6, 17)(8, 10)(11, 12)(14, 15)(16, 18), (2, 3)(5, 17)(6, 11)(8, 9)(12, 18)(13, 16)(14, 20)(15, 19), (1, 9)(2, 10)(3, 4)(7, 8), (1, 2)(3, 7)(4, 8)(5, 11)(9, 10)(12, 13)(14, 15) orbits: { 1, 9, 2, 8, 4, 10, 3, 7 }, { 5, 11, 12, 13, 17, 6, 18, 16 }, { 14, 15, 20, 19 } code no 8: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 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 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 10)(5, 13)(6, 18)(8, 9)(11, 12)(16, 17), (4, 9)(5, 12)(6, 17)(8, 10)(11, 13)(16, 18), (4, 5)(8, 11)(9, 12)(10, 13)(19, 20), (3, 7)(4, 8)(5, 11)(6, 16), (1, 2)(3, 7)(4, 8)(5, 11)(9, 10)(12, 13)(14, 15) orbits: { 1, 2 }, { 3, 7 }, { 4, 10, 9, 5, 8, 13, 12, 11 }, { 6, 18, 17, 16 }, { 14, 15 }, { 19, 20 } code no 9: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 2 elements: ( 1 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 0 0 1 0 0 0 0 0 0 1 , 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8)(12, 14)(13, 15)(17, 18), (1, 7)(2, 3)(4, 8)(5, 13)(9, 10)(11, 12)(14, 15)(18, 19) orbits: { 1, 7, 8, 4, 3, 2 }, { 5, 13, 15, 14, 12, 11 }, { 6 }, { 9, 10 }, { 16 }, { 17, 18, 19 }, { 20 } code no 10: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 1 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 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(8, 11)(9, 12)(10, 13)(18, 19), (3, 7)(4, 8)(5, 11)(6, 16), (3, 8, 5, 7, 4, 11)(6, 16)(9, 14, 12)(10, 15, 13)(17, 18, 19), (1, 2)(6, 16)(9, 10)(12, 13)(14, 15), (1, 15, 9, 13)(2, 14, 10, 12)(3, 8)(4, 7)(5, 11)(17, 19, 18, 20) orbits: { 1, 2, 13, 12, 10, 15, 9, 14 }, { 3, 7, 11, 8, 5, 4 }, { 6, 16 }, { 17, 19, 20, 18 } code no 11: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 1 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 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 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 0 0 1 0 0 0 0 0 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(8, 11)(9, 12)(10, 13)(18, 19), (3, 7)(4, 8)(5, 11)(6, 16), (3, 4)(7, 8)(12, 14)(13, 15)(17, 18), (1, 2)(6, 16)(9, 10)(12, 13)(14, 15), (1, 14)(2, 15)(4, 11)(5, 8)(6, 16)(9, 10)(12, 13)(17, 20) orbits: { 1, 2, 14, 15, 12, 13, 9, 10 }, { 3, 7, 4, 8, 5, 11 }, { 6, 16 }, { 17, 18, 20, 19 } code no 12: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 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 0 0 1 , 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 , 1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 ) acting on the columns of the generator matrix as follows (in order): (6, 16)(17, 18)(19, 20), (4, 9)(5, 12)(6, 16)(8, 10)(11, 13), (4, 5)(8, 11)(9, 12)(10, 13)(17, 19)(18, 20), (1, 7)(2, 3)(4, 10)(5, 11)(6, 16)(8, 9)(12, 13)(14, 15)(17, 18), (1, 8)(2, 4)(3, 10)(5, 11)(6, 17)(7, 9)(12, 13)(14, 15)(16, 18), (1, 10, 5, 2, 9, 11)(3, 8, 12, 7, 4, 13)(6, 17, 19, 16, 18, 20)(14, 15) orbits: { 1, 7, 8, 11, 9, 12, 10, 3, 13, 5, 4, 2 }, { 6, 16, 17, 20, 18, 19 }, { 14, 15 } code no 13: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 32 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 , 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 11)(6, 16)(12, 13)(14, 15)(17, 18)(19, 20), (4, 9)(5, 12)(6, 16)(8, 10)(11, 13), (1, 7)(2, 3)(4, 10)(5, 11)(6, 16)(8, 9)(12, 13)(14, 15)(17, 18), (1, 8)(2, 4)(3, 10)(5, 11)(6, 17)(7, 9)(12, 13)(14, 15)(16, 18) orbits: { 1, 7, 8, 9, 10, 4, 3, 2 }, { 5, 11, 12, 13 }, { 6, 16, 17, 18 }, { 14, 15 }, { 19, 20 } code no 14: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 144 and is strongly generated by the following 5 elements: ( 1 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 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 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 1 0 0 , 1 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 1 1 1 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 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6)(11, 15)(12, 16)(13, 17)(14, 18), (4, 6)(8, 15)(9, 16)(10, 17)(14, 19), (3, 7)(9, 10)(12, 13)(16, 17), (2, 7, 3)(8, 10, 9)(11, 13, 12)(15, 17, 16), (1, 6, 5)(2, 17, 11, 7, 15, 13)(3, 16, 12)(8, 10)(14, 18, 20) orbits: { 1, 5, 6, 4 }, { 2, 3, 13, 7, 12, 17, 11, 15, 16, 10, 8, 9 }, { 14, 18, 19, 20 } code no 15: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 64 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 11)(9, 10)(12, 13)(17, 18)(19, 20), (4, 11)(5, 8)(9, 13)(10, 12)(17, 20)(18, 19), (3, 7)(4, 8)(5, 11)(6, 15), (3, 8)(4, 7)(5, 15)(6, 11)(12, 17)(13, 18)(14, 16), (3, 6)(4, 8)(5, 11)(7, 15)(9, 18)(10, 17)(12, 20)(13, 19), (1, 2)(3, 7)(5, 11)(12, 13)(17, 18) orbits: { 1, 2 }, { 3, 7, 8, 6, 4, 15, 5, 11 }, { 9, 10, 13, 18, 12, 17, 19, 20 }, { 14, 16 } code no 16: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 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 1 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 1 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(4, 5)(8, 12)(9, 11)(10, 13)(15, 16)(17, 19)(18, 20), (1, 2)(3, 7)(5, 11)(12, 13)(17, 18), (1, 7)(4, 11)(5, 9)(8, 13)(10, 12)(15, 16)(17, 20)(18, 19) orbits: { 1, 2, 7, 3 }, { 4, 5, 11, 9 }, { 6 }, { 8, 12, 13, 10 }, { 14 }, { 15, 16 }, { 17, 19, 18, 20 } code no 17: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 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 1 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 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6)(7, 8)(11, 15)(12, 17)(13, 18)(14, 16), (3, 7)(4, 8)(5, 11)(6, 15), (1, 9)(2, 10)(3, 7)(4, 8)(5, 15)(6, 11)(12, 17)(13, 18)(14, 16)(19, 20) orbits: { 1, 9 }, { 2, 10 }, { 3, 4, 7, 8 }, { 5, 6, 11, 15 }, { 12, 17 }, { 13, 18 }, { 14, 16 }, { 19, 20 } code no 18: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 , 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 11)(9, 10)(12, 13)(16, 17)(18, 19), (4, 11)(5, 8)(9, 13)(10, 12)(16, 19)(17, 18), (3, 7)(4, 8)(5, 11)(6, 15), (3, 15)(6, 7)(9, 17)(10, 16)(12, 19)(13, 18), (1, 8)(2, 4)(3, 10)(6, 17)(7, 9)(15, 16), (1, 5, 2, 11)(3, 18, 7, 19)(4, 8)(6, 12, 15, 13)(9, 17)(10, 16) orbits: { 1, 8, 11, 4, 5, 2 }, { 3, 7, 15, 10, 19, 6, 9, 18, 16, 12, 17, 13 }, { 14 }, { 20 } code no 19: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 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 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 , 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 6)(7, 16)(9, 15)(10, 17)(11, 14)(12, 18)(13, 20), (1, 8)(2, 4)(3, 10)(6, 17)(7, 9)(15, 16), (1, 4)(2, 8)(3, 9)(6, 16)(7, 10)(15, 17) orbits: { 1, 8, 4, 2 }, { 3, 6, 10, 9, 17, 16, 7, 15 }, { 5 }, { 11, 14 }, { 12, 18 }, { 13, 20 }, { 19 } code no 20: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 , 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(4, 5)(8, 11)(9, 13)(10, 12)(16, 18)(17, 19), (1, 4)(2, 9)(3, 8)(6, 16)(7, 10)(11, 12)(15, 17), (1, 2)(4, 13)(5, 9)(6, 15)(8, 12)(10, 11)(16, 19)(17, 18) orbits: { 1, 4, 2, 5, 13, 9 }, { 3, 7, 8, 10, 11, 12 }, { 6, 16, 15, 18, 19, 17 }, { 14 }, { 20 } code no 21: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 23040 and is strongly generated by the following 11 elements: ( 1 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 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 , 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 , 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 14)(15, 16)(17, 18)(19, 20), (5, 11)(6, 14)(12, 13)(15, 16), (5, 12)(6, 16)(11, 13)(14, 15)(17, 20)(18, 19), (4, 8)(6, 14)(9, 10)(17, 18), (4, 11)(5, 8)(9, 13)(10, 12)(15, 18)(16, 17), (4, 10)(5, 12)(6, 19, 14, 20)(8, 9)(11, 13)(15, 18, 16, 17), (3, 4)(5, 14)(6, 11)(7, 8)(12, 16)(13, 15), (3, 8)(4, 7)(5, 14)(6, 11)(12, 15)(13, 16), (1, 10)(2, 9)(5, 15)(6, 13)(11, 16)(12, 14), (1, 12, 8, 17, 2, 13, 4, 18)(3, 9, 16, 6)(5, 11)(7, 10, 15, 14), (1, 6, 9, 18, 11, 20)(2, 14, 10, 17, 5, 19)(3, 13, 4)(7, 12, 8) orbits: { 1, 10, 18, 20, 9, 12, 4, 7, 14, 17, 19, 15, 11, 13, 8, 2, 3, 6, 5, 16 } code no 22: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 384 and is strongly generated by the following 8 elements: ( 1 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 1 0 1 0 0 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 , 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 , 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 15)(14, 16)(17, 19)(18, 20), (5, 11)(6, 14)(12, 13)(15, 16), (5, 12)(11, 13)(17, 18)(19, 20), (3, 4)(5, 14)(6, 11)(7, 8)(12, 16)(13, 15)(18, 19), (2, 4)(5, 18, 11, 20)(6, 14, 16, 15)(7, 9)(12, 17, 13, 19), (1, 8)(2, 4)(3, 10)(6, 16)(7, 9)(14, 15), (1, 9)(2, 10)(3, 4)(5, 12)(6, 15)(7, 8)(11, 13)(14, 16), (1, 10)(2, 9)(3, 8)(4, 7)(5, 12)(6, 16)(11, 13)(14, 15) orbits: { 1, 8, 9, 10, 7, 3, 2, 4 }, { 5, 11, 12, 14, 20, 13, 6, 18, 16, 19, 15, 17 } code no 23: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 128 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 , 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 , 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 11)(6, 14)(12, 13)(15, 16), (4, 8)(5, 13)(6, 14)(9, 10)(11, 12)(17, 18)(19, 20), (3, 4)(5, 14)(6, 11)(7, 8)(12, 16)(13, 15)(18, 19), (3, 4, 7, 8)(5, 16, 13, 6, 11, 15, 12, 14)(9, 10)(17, 19, 20, 18), (1, 9)(2, 10)(3, 4)(5, 12)(6, 15)(7, 8)(11, 13)(14, 16), (1, 10)(2, 9)(3, 8)(4, 7)(5, 12)(6, 16)(11, 13)(14, 15), (1, 8)(2, 4)(3, 10)(6, 16)(7, 9)(14, 15) orbits: { 1, 9, 10, 8, 2, 7, 3, 4 }, { 5, 11, 13, 14, 12, 6, 15, 16 }, { 17, 18, 19, 20 } code no 24: ================ 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 120 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(4, 6)(7, 12)(8, 17)(9, 15)(10, 18)(13, 14)(16, 19), (2, 10, 9)(4, 7, 8)(5, 15, 18)(6, 17, 12)(11, 16, 19)(13, 14, 20), (1, 2)(3, 8)(4, 7)(6, 14)(9, 10)(12, 13)(15, 16)(18, 19), (1, 14)(2, 17, 15, 4)(3, 19)(5, 12, 10, 8)(6, 11, 7, 16)(9, 13, 18, 20) orbits: { 1, 2, 14, 5, 9, 4, 13, 6, 18, 8, 15, 10, 20, 7, 12, 16, 19, 17, 3, 11 }