the 19 isometry classes of irreducible [6,2,5]_25 codes are: code no 1: ================ 1 1 1 1 4 0 4 3 2 1 0 4 the automorphism group has order 240 and is strongly generated by the following 7 elements: ( 24 0 0 0 0 24 0 0 0 0 24 0 0 0 0 24 , 1 , 2 0 0 0 0 3 0 0 4 4 4 4 4 3 2 1 , 1 , 16 0 0 0 0 23 0 0 0 0 0 7 16 16 16 16 , 0 , 20 0 0 0 5 5 5 5 0 0 0 20 0 0 20 0 , 0 , 12 0 0 0 0 0 0 12 0 12 0 0 18 18 18 18 , 0 , 0 0 13 0 0 0 0 13 17 17 17 17 13 0 0 0 , 1 , 1 2 3 4 0 4 0 0 0 0 0 2 0 0 3 0 , 0 ) acting on the columns of the generator matrix as follows (in order): id, (3, 5)(4, 6), (3, 6, 5, 4), (2, 5)(3, 4), (2, 3, 5, 4), (1, 4, 2, 5, 3), (1, 6)(3, 4) orbits: { 1, 3, 6, 5, 4, 2 } code no 2: ================ 1 1 1 1 4 0 5 3 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 13 0 0 0 0 14 0 0 7 7 7 7 10 14 16 23 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 5)(4, 6) orbits: { 1 }, { 2 }, { 3, 5 }, { 4, 6 } code no 3: ================ 1 1 1 1 4 0 6 5 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 24 0 0 0 0 11 0 0 0 0 0 13 0 0 21 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6) orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 6 } code no 4: ================ 1 1 1 1 4 0 7 5 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 12 17 21 0 0 12 0 0 17 0 0 1 1 1 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 6)(2, 3)(4, 5) orbits: { 1, 6 }, { 2, 3 }, { 4, 5 } code no 5: ================ 1 1 1 1 4 0 8 5 2 1 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 12 0 0 0 0 22 0 0 5 5 5 5 13 3 15 20 , 1 , 0 12 0 0 12 0 0 0 18 18 18 18 0 0 0 12 , 1 , 12 5 23 14 0 0 0 21 0 0 12 0 23 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 5)(4, 6), (1, 2)(3, 5), (1, 4, 2, 6) orbits: { 1, 2, 6, 4 }, { 3, 5 } code no 6: ================ 1 1 1 1 4 0 9 5 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 22 22 22 22 1 8 14 7 0 0 0 1 0 0 24 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(3, 4) orbits: { 1, 5 }, { 2, 6 }, { 3, 4 } code no 7: ================ 1 1 1 1 4 0 12 5 2 1 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 } code no 8: ================ 1 1 1 1 4 0 19 5 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 9 0 0 0 0 3 0 0 0 0 0 20 0 0 15 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6) orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 6 } code no 9: ================ 1 1 1 1 4 0 24 5 2 1 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 21 0 0 0 0 7 0 0 4 4 4 4 5 24 2 1 , 1 , 14 0 0 0 0 1 0 0 0 0 0 15 0 0 5 0 , 1 , 0 11 0 0 11 0 0 0 0 0 11 0 0 0 0 11 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 5)(4, 6), (3, 4)(5, 6), (1, 2) orbits: { 1, 2 }, { 3, 5, 4, 6 } code no 10: ================ 1 1 1 1 4 0 9 6 2 1 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 } code no 11: ================ 1 1 1 1 4 0 10 6 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 0 2 1 1 1 1 20 12 4 2 9 0 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 5)(3, 6) orbits: { 1, 4 }, { 2, 5 }, { 3, 6 } code no 12: ================ 1 1 1 1 4 0 11 6 2 1 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 17 0 0 0 0 16 0 0 0 0 0 15 0 0 5 0 , 1 , 0 20 0 0 12 0 0 0 4 16 11 8 19 19 19 19 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6), (1, 2)(3, 6)(4, 5) orbits: { 1, 2 }, { 3, 4, 6, 5 } code no 13: ================ 1 1 1 1 4 0 12 6 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 0 17 0 0 9 0 0 11 0 0 22 0 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 3)(5, 6) orbits: { 1, 4 }, { 2, 3 }, { 5, 6 } code no 14: ================ 1 1 1 1 4 0 13 6 2 1 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 0 15 0 0 6 0 0 0 0 0 3 0 21 12 4 2 , 0 , 0 0 0 22 3 15 16 23 10 10 10 10 17 0 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(4, 6), (1, 4)(2, 6)(3, 5) orbits: { 1, 2, 4, 6 }, { 3, 5 } code no 15: ================ 1 1 1 1 4 0 19 6 2 1 0 4 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 22 0 0 0 0 15 0 0 0 0 0 2 0 0 4 0 , 1 , 0 0 0 20 5 5 5 5 0 0 20 0 20 0 0 0 , 1 , 0 8 0 0 19 0 0 0 21 7 10 5 15 15 15 15 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6), (1, 4)(2, 5), (1, 2)(3, 6)(4, 5) orbits: { 1, 4, 2, 3, 5, 6 } code no 16: ================ 1 1 1 1 4 0 20 6 2 1 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 11 0 0 0 0 6 0 0 0 0 0 17 0 0 9 0 , 1 , 0 19 0 0 19 0 0 0 0 0 19 0 0 0 0 19 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6), (1, 2) orbits: { 1, 2 }, { 3, 4 }, { 5, 6 } code no 17: ================ 1 1 1 1 4 0 10 9 2 1 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 8 0 0 6 0 0 0 14 12 15 20 10 10 10 10 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(3, 6)(4, 5) orbits: { 1, 2 }, { 3, 6 }, { 4, 5 } code no 18: ================ 1 1 1 1 4 0 23 9 2 1 0 4 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 21 0 0 0 0 21 0 0 9 9 9 9 0 0 0 21 , 1 , 0 15 0 0 15 0 0 0 10 10 10 10 0 0 0 15 , 0 , 7 7 7 7 0 0 7 0 0 24 0 0 17 4 16 23 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 5), (1, 2)(3, 5), (1, 5)(2, 3)(4, 6) orbits: { 1, 2, 5, 3 }, { 4, 6 } code no 19: ================ 1 1 1 1 4 0 13 6 5 1 0 4 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 0 0 20 0 0 0 0 4 17 0 0 0 0 24 0 0 , 0 , 22 22 22 22 0 0 20 0 0 17 0 0 10 16 13 8 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 4)(5, 6), (1, 5)(2, 3)(4, 6) orbits: { 1, 3, 5, 2, 6, 4 }