the 42 isometry classes of irreducible [23,20,3]_5 codes are: code no 1: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 40 and is strongly generated by the following 3 elements: ( 1 0 0 0 4 0 4 0 4 , 2 0 0 1 2 0 2 0 2 , 1 0 0 3 4 2 1 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(4, 13)(5, 8)(6, 7)(10, 12)(14, 16)(17, 18)(19, 21)(22, 23), (2, 6, 8, 5, 7)(3, 12, 11, 10, 9)(4, 14, 15, 16, 13)(17, 20, 18, 21, 19), (2, 12, 16, 21)(3, 4, 19, 5)(6, 9, 15, 17)(7, 10, 13, 20)(8, 11, 14, 18) orbits: { 1 }, { 2, 7, 21, 6, 5, 20, 19, 18, 16, 17, 8, 13, 4, 14, 15, 12, 10, 3, 11, 9 }, { 22, 23 } code no 2: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 32 and is strongly generated by the following 3 elements: ( 4 0 0 0 3 0 0 0 3 , 4 0 0 0 3 0 0 4 2 , 1 0 0 0 4 2 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (4, 14, 16, 15)(5, 6, 8, 7)(9, 10, 12, 11)(18, 19, 21, 20), (3, 17)(4, 15, 16, 14)(5, 6, 8, 7)(9, 20, 12, 19)(10, 18, 11, 21)(22, 23), (2, 3, 13, 17)(4, 21, 7, 11)(5, 9, 14, 20)(6, 10, 16, 18)(8, 12, 15, 19) orbits: { 1 }, { 2, 17, 3, 13 }, { 4, 15, 14, 11, 16, 12, 9, 18, 7, 10, 20, 8, 19, 5, 21, 6 }, { 22, 23 } code no 3: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 4 1 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(4, 15)(5, 7)(9, 12)(10, 11)(13, 16)(17, 20)(18, 19)(21, 23) orbits: { 1 }, { 2, 8 }, { 3 }, { 4, 15 }, { 5, 7 }, { 6 }, { 9, 12 }, { 10, 11 }, { 13, 16 }, { 14 }, { 17, 20 }, { 18, 19 }, { 21, 23 }, { 22 } code no 4: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 5: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 6: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 3 1 0 2 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 7)(3, 10)(4, 16)(5, 6)(11, 12)(14, 15)(17, 20)(18, 19)(21, 22) orbits: { 1 }, { 2, 7 }, { 3, 10 }, { 4, 16 }, { 5, 6 }, { 8 }, { 9 }, { 11, 12 }, { 13 }, { 14, 15 }, { 17, 20 }, { 18, 19 }, { 21, 22 }, { 23 } code no 7: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 8: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 4 0 0 0 1 0 2 0 1 , 2 0 0 4 0 4 3 4 0 ) acting on the columns of the generator matrix as follows (in order): (3, 10)(5, 8)(6, 7)(11, 12)(13, 14)(15, 16)(17, 19)(20, 22), (2, 9)(3, 7, 10, 6)(5, 11, 8, 12)(13, 16, 14, 15)(17, 20, 19, 22)(18, 21) orbits: { 1 }, { 2, 9 }, { 3, 10, 6, 7 }, { 4 }, { 5, 8, 12, 11 }, { 13, 14, 15, 16 }, { 17, 19, 22, 20 }, { 18, 21 }, { 23 } code no 9: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 4 0 0 4 1 0 4 0 1 , 1 0 0 0 0 1 0 1 0 , 0 3 2 3 0 2 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 12)(4, 14)(5, 7)(9, 11)(13, 15)(17, 19)(20, 21), (2, 3)(5, 9)(6, 10)(7, 11)(8, 12)(17, 20)(18, 22)(19, 21), (1, 23)(2, 12)(4, 22)(5, 19)(6, 15)(7, 21)(9, 17)(10, 13)(11, 20)(14, 18) orbits: { 1, 23 }, { 2, 8, 3, 12 }, { 4, 14, 22, 18 }, { 5, 7, 9, 19, 11, 21, 17, 20 }, { 6, 10, 15, 13 }, { 16 } code no 10: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 4 0 1 4 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 8)(4, 14)(5, 11)(6, 10)(7, 9)(13, 15)(17, 21)(18, 22)(19, 20) orbits: { 1 }, { 2, 12 }, { 3, 8 }, { 4, 14 }, { 5, 11 }, { 6, 10 }, { 7, 9 }, { 13, 15 }, { 16 }, { 17, 21 }, { 18, 22 }, { 19, 20 }, { 23 } code no 11: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 4 0 1 4 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 8)(4, 14)(5, 11)(6, 10)(7, 9)(13, 15)(17, 21)(18, 22)(19, 20) orbits: { 1 }, { 2, 12 }, { 3, 8 }, { 4, 14 }, { 5, 11 }, { 6, 10 }, { 7, 9 }, { 13, 15 }, { 16 }, { 17, 21 }, { 18, 22 }, { 19, 20 }, { 23 } code no 12: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 1 0 1 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(6, 7)(9, 13)(10, 17)(11, 20)(12, 22)(14, 18)(15, 21)(16, 23) orbits: { 1, 2 }, { 3 }, { 4 }, { 5 }, { 6, 7 }, { 8 }, { 9, 13 }, { 10, 17 }, { 11, 20 }, { 12, 22 }, { 14, 18 }, { 15, 21 }, { 16, 23 }, { 19 } code no 13: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 1 4 4 3 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 16)(3, 11)(4, 6)(5, 13)(7, 14)(8, 15)(9, 10)(20, 23)(21, 22) orbits: { 1 }, { 2, 16 }, { 3, 11 }, { 4, 6 }, { 5, 13 }, { 7, 14 }, { 8, 15 }, { 9, 10 }, { 12 }, { 17 }, { 18 }, { 19 }, { 20, 23 }, { 21, 22 } code no 14: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 15: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 4 4 4 2 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 10)(5, 14)(6, 15)(7, 16)(8, 13)(11, 12)(20, 23)(21, 22) orbits: { 1 }, { 2, 4 }, { 3, 10 }, { 5, 14 }, { 6, 15 }, { 7, 16 }, { 8, 13 }, { 9 }, { 11, 12 }, { 17 }, { 18 }, { 19 }, { 20, 23 }, { 21, 22 } code no 16: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 4 4 4 0 0 1 , 4 0 0 3 4 4 4 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(5, 13)(6, 16)(7, 15)(8, 14)(17, 19)(20, 23)(21, 22), (2, 14)(3, 12)(4, 8)(5, 15)(6, 16)(7, 13)(9, 11)(20, 22)(21, 23) orbits: { 1 }, { 2, 4, 14, 8 }, { 3, 12 }, { 5, 13, 15, 7 }, { 6, 16 }, { 9, 11 }, { 10 }, { 17, 19 }, { 18 }, { 20, 23, 22, 21 } code no 17: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 0 4 4 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 13)(4, 5)(6, 14)(7, 15)(8, 16)(9, 12)(10, 11)(20, 22)(21, 23) orbits: { 1 }, { 2, 13 }, { 3 }, { 4, 5 }, { 6, 14 }, { 7, 15 }, { 8, 16 }, { 9, 12 }, { 10, 11 }, { 17 }, { 18 }, { 19 }, { 20, 22 }, { 21, 23 } code no 18: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 0 2 4 4 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 15)(3, 9)(4, 7)(5, 16)(6, 13)(8, 14)(10, 12)(20, 23)(21, 22) orbits: { 1 }, { 2, 15 }, { 3, 9 }, { 4, 7 }, { 5, 16 }, { 6, 13 }, { 8, 14 }, { 10, 12 }, { 11 }, { 17 }, { 18 }, { 19 }, { 20, 23 }, { 21, 22 } code no 19: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 1 0 0 0 4 0 3 0 4 , 4 0 0 1 1 1 0 0 4 , 4 0 4 0 1 3 2 0 1 ) acting on the columns of the generator matrix as follows (in order): (3, 10)(5, 8)(6, 7)(11, 12)(13, 14)(15, 16)(17, 19)(20, 21)(22, 23), (2, 4)(5, 13)(6, 16)(7, 15)(8, 14)(17, 19)(20, 23)(21, 22), (1, 9)(2, 19, 4, 17)(3, 10)(5, 22, 13, 21)(6, 7, 16, 15)(8, 20, 14, 23) orbits: { 1, 9 }, { 2, 4, 17, 19 }, { 3, 10 }, { 5, 8, 13, 21, 14, 23, 22, 20 }, { 6, 7, 16, 15 }, { 11, 12 }, { 18 } code no 20: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 1 0 0 0 4 0 2 0 4 , 4 0 0 0 2 0 2 0 2 , 1 0 0 2 0 3 1 3 0 ) acting on the columns of the generator matrix as follows (in order): (3, 11)(4, 14)(5, 8)(6, 7)(9, 10)(13, 15)(16, 19)(17, 18)(20, 23)(21, 22), (3, 10, 11, 9)(4, 13, 14, 15)(5, 7, 8, 6)(16, 18, 19, 17)(20, 22, 23, 21), (2, 12)(3, 7, 11, 6)(4, 13, 14, 15)(5, 10, 8, 9)(16, 23, 19, 20)(17, 22, 18, 21) orbits: { 1 }, { 2, 12 }, { 3, 11, 9, 6, 10, 7, 8, 5 }, { 4, 14, 15, 13 }, { 16, 19, 17, 20, 18, 23, 21, 22 } code no 21: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 0 0 2 0 1 3 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 10)(3, 7)(5, 11)(6, 12)(8, 9)(16, 21)(17, 23)(18, 22)(19, 20) orbits: { 1 }, { 2, 10 }, { 3, 7 }, { 4 }, { 5, 11 }, { 6, 12 }, { 8, 9 }, { 13 }, { 14 }, { 15 }, { 16, 21 }, { 17, 23 }, { 18, 22 }, { 19, 20 } code no 22: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 1 0 1 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(6, 7)(9, 13)(10, 16)(11, 20)(12, 23)(14, 17)(15, 21)(19, 22) orbits: { 1, 2 }, { 3 }, { 4 }, { 5 }, { 6, 7 }, { 8 }, { 9, 13 }, { 10, 16 }, { 11, 20 }, { 12, 23 }, { 14, 17 }, { 15, 21 }, { 18 }, { 19, 22 } code no 23: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 24: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 0 3 0 2 4 1 3 3 0 ) acting on the columns of the generator matrix as follows (in order): (1, 12, 23, 2)(3, 4, 18, 5)(6, 10)(7, 9, 19, 22)(8, 11, 20, 14)(13, 15, 21, 16) orbits: { 1, 2, 23, 12 }, { 3, 5, 18, 4 }, { 6, 10 }, { 7, 22, 19, 9 }, { 8, 14, 20, 11 }, { 13, 16, 21, 15 }, { 17 } code no 25: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 2 4 2 3 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (1, 12)(2, 23)(6, 13)(7, 22)(8, 17)(9, 10)(14, 20)(15, 19)(16, 21) orbits: { 1, 12 }, { 2, 23 }, { 3 }, { 4 }, { 5 }, { 6, 13 }, { 7, 22 }, { 8, 17 }, { 9, 10 }, { 11 }, { 14, 20 }, { 15, 19 }, { 16, 21 }, { 18 } code no 26: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 27: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 28: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 3 2 0 1 2 0 4 4 ) acting on the columns of the generator matrix as follows (in order): (1, 23)(2, 20)(3, 13)(5, 14)(6, 17)(7, 11)(9, 19)(12, 21)(15, 18) orbits: { 1, 23 }, { 2, 20 }, { 3, 13 }, { 4 }, { 5, 14 }, { 6, 17 }, { 7, 11 }, { 8 }, { 9, 19 }, { 10 }, { 12, 21 }, { 15, 18 }, { 16 }, { 22 } code no 29: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 4 0 0 4 0 0 4 1 ) acting on the columns of the generator matrix as follows (in order): (1, 8)(3, 22)(4, 17)(5, 6)(9, 21)(10, 18)(11, 15)(13, 20)(19, 23) orbits: { 1, 8 }, { 2 }, { 3, 22 }, { 4, 17 }, { 5, 6 }, { 7 }, { 9, 21 }, { 10, 18 }, { 11, 15 }, { 12 }, { 13, 20 }, { 14 }, { 16 }, { 19, 23 } code no 30: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 31: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 32: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 4 1 0 3 1 0 2 2 ) acting on the columns of the generator matrix as follows (in order): (1, 23)(2, 20)(3, 13)(5, 14)(6, 17)(7, 11)(9, 19)(12, 21)(15, 18) orbits: { 1, 23 }, { 2, 20 }, { 3, 13 }, { 4 }, { 5, 14 }, { 6, 17 }, { 7, 11 }, { 8 }, { 9, 19 }, { 10 }, { 12, 21 }, { 15, 18 }, { 16 }, { 22 } code no 33: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 4 1 4 2 2 4 3 1 ) acting on the columns of the generator matrix as follows (in order): (1, 23)(2, 14)(3, 22)(5, 16)(6, 12)(8, 21)(9, 13)(10, 18)(15, 17)(19, 20) orbits: { 1, 23 }, { 2, 14 }, { 3, 22 }, { 4 }, { 5, 16 }, { 6, 12 }, { 7 }, { 8, 21 }, { 9, 13 }, { 10, 18 }, { 11 }, { 15, 17 }, { 19, 20 } code no 34: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }, { 15 }, { 16 }, { 17 }, { 18 }, { 19 }, { 20 }, { 21 }, { 22 }, { 23 } code no 35: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 4 2 2 0 3 2 1 2 ) acting on the columns of the generator matrix as follows (in order): (1, 17)(2, 12)(3, 20)(4, 11)(6, 23)(7, 21)(8, 13)(10, 22)(15, 19)(16, 18) orbits: { 1, 17 }, { 2, 12 }, { 3, 20 }, { 4, 11 }, { 5 }, { 6, 23 }, { 7, 21 }, { 8, 13 }, { 9 }, { 10, 22 }, { 14 }, { 15, 19 }, { 16, 18 } code no 36: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 4 0 0 4 0 1 4 1 0 , 4 0 0 4 1 0 4 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 8)(4, 14)(5, 11)(6, 10)(7, 9)(13, 15)(16, 20)(17, 21)(18, 19), (2, 8)(3, 12)(4, 14)(5, 7)(9, 11)(13, 15)(16, 18)(19, 20)(22, 23) orbits: { 1 }, { 2, 12, 8, 3 }, { 4, 14 }, { 5, 11, 7, 9 }, { 6, 10 }, { 13, 15 }, { 16, 20, 18, 19 }, { 17, 21 }, { 22, 23 } code no 37: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 4 0 0 4 0 1 4 1 0 , 4 0 0 4 1 0 4 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 8)(4, 14)(5, 11)(6, 10)(7, 9)(13, 15)(16, 20)(17, 21)(18, 19), (2, 8)(3, 12)(4, 14)(5, 7)(9, 11)(13, 15)(16, 18)(19, 20)(22, 23) orbits: { 1 }, { 2, 12, 8, 3 }, { 4, 14 }, { 5, 11, 7, 9 }, { 6, 10 }, { 13, 15 }, { 16, 20, 18, 19 }, { 17, 21 }, { 22, 23 } code no 38: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 3 0 4 0 4 0 2 ) acting on the columns of the generator matrix as follows (in order): (1, 9)(3, 10)(4, 7)(5, 20)(6, 21)(8, 17)(13, 18)(14, 19)(15, 23)(16, 22) orbits: { 1, 9 }, { 2 }, { 3, 10 }, { 4, 7 }, { 5, 20 }, { 6, 21 }, { 8, 17 }, { 11 }, { 12 }, { 13, 18 }, { 14, 19 }, { 15, 23 }, { 16, 22 } code no 39: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 1 3 0 1 0 4 2 2 , 2 3 0 3 0 1 4 2 0 ) acting on the columns of the generator matrix as follows (in order): (1, 17)(3, 14)(4, 7)(5, 21)(6, 20)(8, 9)(10, 19)(12, 23)(13, 22)(16, 18), (1, 9, 17, 8)(2, 11)(3, 20, 14, 6)(4, 23, 7, 12)(5, 10, 21, 19)(13, 16, 22, 18) orbits: { 1, 17, 8, 9 }, { 2, 11 }, { 3, 14, 6, 20 }, { 4, 7, 12, 23 }, { 5, 21, 19, 10 }, { 13, 22, 18, 16 }, { 15 } code no 40: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 4 0 0 1 0 4 4 4 0 , 0 4 4 4 0 1 0 0 4 , 0 0 1 0 1 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 5)(6, 9)(7, 10)(8, 11)(16, 20)(17, 19)(18, 21)(22, 23), (1, 13)(2, 12)(6, 17)(7, 23)(8, 20)(9, 19)(10, 22)(11, 16)(14, 15), (1, 3)(5, 13)(6, 19)(7, 16)(8, 22)(10, 11)(14, 21)(15, 18)(20, 23) orbits: { 1, 13, 3, 5 }, { 2, 12 }, { 4 }, { 6, 9, 17, 19 }, { 7, 10, 23, 16, 22, 11, 20, 8 }, { 14, 15, 21, 18 } code no 41: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 4 0 0 4 0 1 4 1 0 , 1 0 0 2 4 0 0 0 4 , 1 0 0 1 0 3 3 2 0 ) acting on the columns of the generator matrix as follows (in order): (2, 12)(3, 8)(4, 14)(5, 11)(6, 10)(7, 9)(13, 15)(16, 18)(17, 19), (2, 7)(4, 14)(5, 6)(9, 12)(10, 11)(13, 15)(16, 17)(18, 19)(20, 21)(22, 23), (2, 10)(3, 8)(4, 20)(5, 12)(6, 9)(7, 11)(13, 22)(14, 21)(15, 23)(18, 19) orbits: { 1 }, { 2, 12, 7, 10, 9, 5, 11, 6 }, { 3, 8 }, { 4, 14, 20, 21 }, { 13, 15, 22, 23 }, { 16, 18, 17, 19 } code no 42: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 40 and is strongly generated by the following 3 elements: ( 1 0 0 0 4 2 0 3 3 , 1 0 0 4 2 0 4 1 1 , 3 2 3 2 4 2 2 2 4 ) acting on the columns of the generator matrix as follows (in order): (2, 11, 3, 18, 14)(4, 10, 19, 17, 7)(5, 12, 8, 21, 16)(6, 13, 9, 20, 15), (2, 5, 7, 6)(3, 16, 19, 13)(4, 9, 14, 21)(8, 17, 20, 11)(10, 15, 18, 12), (1, 22)(2, 5, 17, 15)(3, 12, 10, 20)(4, 6, 18, 16)(7, 9, 14, 8)(11, 21, 19, 13) orbits: { 1, 22 }, { 2, 14, 6, 15, 18, 9, 7, 4, 20, 10, 17, 3, 13, 5, 8, 21, 16, 12, 19, 11 }, { 23 }