the 1 isometry classes of irreducible [6,3,4]_5 codes are: code no 1: ================ 1 1 1 4 0 0 3 2 1 0 4 0 4 3 1 0 0 4 the automorphism group has order 120 and is strongly generated by the following 5 elements: ( 4 0 0 0 4 0 4 3 1 , 4 0 0 0 1 0 3 3 3 , 1 0 0 4 1 3 0 4 0 , 0 0 2 2 0 0 3 3 3 , 3 1 2 3 0 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (3, 6)(4, 5), (3, 5, 6, 4), (2, 3, 4, 5), (1, 2, 4, 3), (1, 2, 5, 6) orbits: { 1, 3, 6, 4, 2, 5 }