the 4 isometry classes of irreducible [5,2,4]_27 codes are: code no 1: ================ 1 1 1 2 0 3 2 1 0 2 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 24 0 0 12 12 12 0 24 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3, 4) orbits: { 1 }, { 2, 4, 3 }, { 5 } code no 2: ================ 1 1 1 2 0 4 3 1 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 12 12 12 0 0 24 0 24 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 4)(2, 3) orbits: { 1, 4 }, { 2, 3 }, { 5 } code no 3: ================ 1 1 1 2 0 7 3 1 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 26 0 26 0 0 13 13 13 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(3, 4) orbits: { 1, 2 }, { 3, 4 }, { 5 } code no 4: ================ 1 1 1 2 0 17 3 1 0 2 the automorphism group has order 3 and is strongly generated by the following 1 elements: ( 16 1 24 0 26 0 11 0 0 , 2 ) acting on the columns of the generator matrix as follows (in order): (1, 3, 5) orbits: { 1, 5, 3 }, { 2 }, { 4 }