the 10 isometry classes of irreducible [6,3,3]_8 codes are: code no 1: ================ 1 1 1 1 0 0 1 1 0 0 1 0 2 1 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 7 0 0 0 7 0 7 7 7 , 0 , 7 4 0 3 0 0 4 4 4 , 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (1, 2, 6)(3, 4) orbits: { 1, 6, 2 }, { 3, 4 }, { 5 } code no 2: ================ 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 the automorphism group has order 72 and is strongly generated by the following 6 elements: ( 7 0 0 0 7 0 0 0 7 , 2 , 3 0 0 3 0 3 3 3 0 , 0 , 7 0 0 7 7 0 7 0 7 , 2 , 3 3 3 0 0 3 0 3 0 , 2 , 0 0 3 3 3 3 3 0 0 , 1 , 6 0 6 6 0 0 6 6 6 , 0 ) acting on the columns of the generator matrix as follows (in order): id, (2, 6)(3, 5), (2, 5)(3, 6), (1, 4)(2, 3), (1, 3)(2, 4), (1, 2, 6)(3, 5, 4) orbits: { 1, 4, 3, 6, 2, 5 } code no 3: ================ 1 1 1 1 0 0 1 1 0 0 1 0 2 0 1 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 4 4 0 4 4 4 5 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3, 5)(2, 6, 4) orbits: { 1, 5, 3 }, { 2, 4, 6 } code no 4: ================ 1 1 1 1 0 0 1 1 0 0 1 0 3 2 1 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 0 0 7 7 7 7 7 0 0 , 0 , 0 7 0 7 0 0 7 7 7 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 4), (1, 2)(3, 4) orbits: { 1, 3, 2, 4 }, { 5 }, { 6 } code no 5: ================ 1 1 1 1 0 0 1 1 0 0 1 0 4 2 1 0 0 1 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 } code no 6: ================ 1 1 1 1 0 0 2 1 0 0 1 0 3 1 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 1 0 0 0 1 0 1 1 1 , 0 , 7 0 0 4 3 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (2, 6, 5) orbits: { 1 }, { 2, 5, 6 }, { 3, 4 } code no 7: ================ 1 1 1 1 0 0 2 1 0 0 1 0 6 1 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 0 0 0 1 0 1 1 1 , 0 , 7 0 0 3 4 0 4 4 4 , 1 , 1 3 0 2 0 0 3 3 3 , 2 , 1 4 0 0 5 0 0 0 1 , 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (2, 5, 6)(3, 4), (1, 2, 5)(3, 4), (1, 5, 6) orbits: { 1, 5, 6, 2 }, { 3, 4 } code no 8: ================ 1 1 1 1 0 0 2 1 0 0 1 0 2 2 1 0 0 1 the automorphism group has order 6 and is strongly generated by the following 1 elements: ( 0 0 6 6 6 6 0 1 0 , 2 ) acting on the columns of the generator matrix as follows (in order): (1, 6, 5, 4, 2, 3) orbits: { 1, 3, 2, 4, 5, 6 } code no 9: ================ 1 1 1 1 0 0 2 1 0 0 1 0 3 2 1 0 0 1 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 } code no 10: ================ 1 1 1 1 0 0 2 1 0 0 1 0 3 6 1 0 0 1 the automorphism group has order 9 and is strongly generated by the following 2 elements: ( 2 0 0 0 3 0 2 3 4 , 1 , 1 3 0 2 0 0 0 0 3 , 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4, 6), (1, 2, 5) orbits: { 1, 5, 2 }, { 3, 6, 4 }