the 54 isometry classes of irreducible [7,4,3]_8 codes are: code no 1: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 3 1 0 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 2 0 0 0 2 0 2 2 2 , 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, 7, 6) orbits: { 1 }, { 2, 6, 7 }, { 3, 4 }, { 5 } code no 2: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 6 1 0 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 5 2 0 0 0 2 , 2 , 7 4 0 3 0 0 4 4 4 , 2 , 5 7 0 7 5 0 2 2 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (2, 7, 6), (1, 2, 6)(3, 4), (1, 7)(2, 6)(3, 4) orbits: { 1, 6, 7, 2 }, { 3, 4 }, { 5 } code no 3: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 0 3 0 3 3 0 3 0 3 , 2 ) acting on the columns of the generator matrix as follows (in order): (1, 5, 2)(3, 4, 7) orbits: { 1, 2, 5 }, { 3, 7, 4 }, { 6 } code no 4: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 2 0 1 0 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 }, { 7 } code no 5: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 4 0 1 0 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 }, { 7 } code no 6: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 6 0 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 7 7 0 3 7 0 0 0 5 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3 }, { 4, 7 } code no 7: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 2 2 1 0 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, 7, 6, 4, 2, 3) orbits: { 1, 3, 2, 4, 6, 7 }, { 5 } code no 8: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 3 2 1 0 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 }, { 7 } code no 9: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 6 2 1 0 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 }, { 7 } code no 10: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 3 4 1 0 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 }, { 7 } code no 11: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 1 0 0 0 1 0 3 6 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 5 2 0 7 0 0 0 0 2 , 2 ) acting on the columns of the generator matrix as follows (in order): (1, 2, 6) orbits: { 1, 6, 2 }, { 3 }, { 4 }, { 5 }, { 7 } code no 12: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 the automorphism group has order 504 and is strongly generated by the following 8 elements: ( 7 0 0 0 7 0 0 0 7 , 2 , 2 0 0 0 2 0 0 2 2 , 2 , 2 0 0 0 2 0 2 0 2 , 2 , 7 0 0 7 7 0 7 0 7 , 2 , 7 0 0 7 0 7 7 7 0 , 0 , 4 0 0 4 4 4 4 4 0 , 2 , 6 0 6 6 0 0 6 6 6 , 0 , 0 4 4 4 0 4 0 4 0 , 2 ) acting on the columns of the generator matrix as follows (in order): id, (3, 7)(4, 6), (3, 6)(4, 7), (2, 5)(3, 6), (2, 6)(3, 5), (2, 6, 4)(3, 7, 5), (1, 2, 6)(3, 5, 4), (1, 4, 7)(2, 3, 6) orbits: { 1, 6, 7, 4, 3, 2, 5 } code no 13: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 2 1 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 5 0 0 0 0 5 0 5 0 , 0 , 7 0 0 7 7 0 7 0 7 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 6), (2, 5)(3, 6) orbits: { 1 }, { 2, 3, 5, 6 }, { 4 }, { 7 } code no 14: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 4 2 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 2 0 2 2 0 0 2 2 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 2, 6)(3, 5, 4) orbits: { 1, 6, 2 }, { 3, 4, 5 }, { 7 } code no 15: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 2 1 1 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 6 0 0 6 6 0 1 0 6 , 0 , 3 0 0 0 0 5 3 5 5 , 2 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(3, 6)(4, 7), (2, 4, 6, 5, 7, 3) orbits: { 1 }, { 2, 5, 3, 6, 7, 4 } code no 16: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 4 1 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 7 0 0 4 3 3 3 3 0 , 2 ) acting on the columns of the generator matrix as follows (in order): (2, 6, 7)(3, 4, 5) orbits: { 1 }, { 2, 7, 6 }, { 3, 5, 4 } code no 17: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 5 1 1 0 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 }, { 7 } code no 18: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 1 2 1 0 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 }, { 7 } code no 19: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 3 2 1 0 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 }, { 7 } code no 20: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 5 2 1 0 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 }, { 7 } code no 21: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 7 2 1 0 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 }, { 7 } code no 22: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 4 3 1 0 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 }, { 7 } code no 23: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 6 3 1 0 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 }, { 7 } code no 24: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 7 3 1 0 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 }, { 7 } code no 25: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 2 4 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 6 0 0 0 0 3 0 1 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(4, 7)(5, 6) orbits: { 1 }, { 2, 3 }, { 4, 7 }, { 5, 6 } code no 26: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 2 0 1 0 0 1 0 7 4 1 0 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 }, { 7 } code no 27: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 4 2 1 0 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 }, { 7 } code no 28: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 5 2 1 0 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 }, { 7 } code no 29: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 6 2 1 0 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 }, { 7 } code no 30: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 7 2 1 0 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 }, { 7 } code no 31: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 2 3 1 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 5 elements: ( 2 0 0 0 2 0 6 4 2 , 0 , 7 0 0 0 7 0 7 7 7 , 0 , 0 0 7 7 7 7 7 0 0 , 0 , 0 7 0 7 0 0 7 7 7 , 0 , 3 4 7 4 3 7 7 7 7 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 6)(4, 7), (3, 4)(6, 7), (1, 3)(2, 4), (1, 2)(3, 4), (1, 6, 2, 7)(3, 4) orbits: { 1, 3, 2, 7, 6, 4 }, { 5 } code no 32: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 5 3 1 0 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 }, { 7 } code no 33: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 7 3 1 0 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 }, { 7 } code no 34: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 5 4 1 0 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 }, { 7 } code no 35: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 3 2 1 0 0 1 0 4 5 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 0 7 0 7 0 0 7 7 7 , 0 , 0 0 7 7 7 7 7 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(3, 4), (1, 3)(2, 4) orbits: { 1, 2, 3, 4 }, { 5 }, { 6 }, { 7 } code no 36: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 5 2 1 0 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 }, { 7 } code no 37: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 6 4 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 2 2 2 2 2 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 4)(6, 7) orbits: { 1, 3 }, { 2, 4 }, { 5 }, { 6, 7 } code no 38: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 7 4 1 0 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 }, { 7 } code no 39: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 2 5 1 0 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 }, { 7 } code no 40: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 3 5 1 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 1 elements: ( 6 3 1 2 7 1 0 4 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 4, 6, 2, 3, 7) orbits: { 1, 7, 3, 2, 6, 4 }, { 5 } code no 41: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 6 5 1 0 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 }, { 7 } code no 42: ================ 1 1 1 1 0 0 0 1 1 0 0 1 0 0 4 2 1 0 0 1 0 5 7 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 1 1 1 0 0 1 0 1 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 3)(6, 7) orbits: { 1, 4 }, { 2, 3 }, { 5 }, { 6, 7 } code no 43: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 1 0 0 0 1 0 4 1 0 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 , 0 5 0 6 3 0 6 6 6 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (1, 7, 2)(3, 4) orbits: { 1, 2, 7 }, { 3, 4 }, { 5 }, { 6 } code no 44: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 1 0 0 0 1 0 2 2 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 1 0 0 3 2 0 4 4 4 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 6, 5)(3, 7, 4) orbits: { 1 }, { 2, 5, 6 }, { 3, 4, 7 } code no 45: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 1 0 0 0 1 0 3 2 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 6 3 0 7 6 0 0 0 4 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(2, 6)(4, 7) orbits: { 1, 5 }, { 2, 6 }, { 3 }, { 4, 7 } code no 46: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 1 0 0 0 1 0 5 2 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 5 2 0 0 6 0 6 6 6 , 2 ) acting on the columns of the generator matrix as follows (in order): (1, 6, 5)(3, 7, 4) orbits: { 1, 5, 6 }, { 2 }, { 3, 4, 7 } code no 47: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 6 1 0 0 0 1 0 2 2 1 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 6 7 0 7 7 4 , 2 , 1 2 0 2 1 0 0 0 3 , 0 , 0 2 0 2 0 0 0 0 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 6, 5)(3, 4, 7), (1, 6)(2, 5), (1, 2)(5, 6) orbits: { 1, 6, 2, 5 }, { 3, 7, 4 } code no 48: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 2 2 1 0 0 1 0 4 3 1 0 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 }, { 7 } code no 49: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 2 2 1 0 0 1 0 7 4 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 4 4 5 5 4 2 1 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 6)(3, 5) orbits: { 1, 4 }, { 2, 6 }, { 3, 5 }, { 7 } code no 50: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 2 2 1 0 0 1 0 6 5 1 0 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 }, { 7 } code no 51: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 2 1 0 0 1 0 2 3 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 2 0 6 4 2 , 0 , 3 0 0 0 3 0 3 3 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 6)(4, 7), (3, 4)(6, 7) orbits: { 1 }, { 2 }, { 3, 6, 4, 7 }, { 5 } code no 52: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 2 1 0 0 1 0 7 3 1 0 0 0 1 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 3 0 0 0 7 0 0 0 4 , 2 ) acting on the columns of the generator matrix as follows (in order): (4, 7, 6) orbits: { 1 }, { 2 }, { 3 }, { 4, 6, 7 }, { 5 } code no 53: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 2 1 0 0 1 0 6 5 1 0 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 }, { 7 } code no 54: ================ 1 1 1 1 0 0 0 2 1 0 0 1 0 0 3 6 1 0 0 1 0 2 7 1 0 0 0 1 the automorphism group has order 36 and is strongly generated by the following 4 elements: ( 5 0 0 0 1 0 0 0 7 , 1 , 2 0 0 0 3 0 2 3 4 , 1 , 4 0 0 0 2 0 4 2 1 , 2 , 1 3 0 2 0 0 0 0 3 , 2 ) acting on the columns of the generator matrix as follows (in order): (4, 7, 6), (3, 4, 6), (3, 4, 7), (1, 2, 5) orbits: { 1, 5, 2 }, { 3, 6, 7, 4 }