the 3 isometry classes of irreducible [19,2,11]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 19508428800 and is strongly generated by the following 23 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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9)(11, 12, 16)(13, 17, 14), (6, 8)(11, 13, 14, 12, 16, 15, 17), (6, 8, 7)(9, 10)(11, 15, 16)(12, 17)(13, 14), (5, 7, 10, 8, 9)(13, 16)(14, 15), (4, 6, 9)(11, 14, 16, 17, 12, 13), (4, 12, 7, 13, 5, 11, 9, 16, 18, 19, 6, 15, 8, 14)(10, 17), (2, 3)(4, 7, 8, 5, 10, 6, 9)(11, 16, 13, 17, 12), (1, 3)(5, 8, 7, 9, 10)(11, 17)(13, 14, 16, 15), (1, 2)(4, 5, 18, 10, 7, 8)(6, 9)(11, 17, 14, 16, 15, 12) orbits: { 1, 3, 2 }, { 4, 9, 14, 8, 10, 6, 11, 7, 17, 19, 13, 12, 16, 15, 18, 5 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 4877107200 and is strongly generated by the following 20 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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3, 2 }, { 5, 8, 7, 6, 9, 10, 18 }, { 11, 14, 19, 17, 15, 12, 16, 13 } code no 3: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 3483648000 and is strongly generated by the following 23 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 , 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (17, 19), (16, 17), (15, 17), (14, 17, 16), (14, 16, 17, 15, 19), (13, 17, 15), (12, 17), (12, 14)(15, 17), (12, 16), (11, 13)(14, 15), (11, 14, 12, 16, 15, 17, 19), (10, 18)(11, 12, 15, 13, 17, 14, 16), (9, 10)(11, 12)(13, 15, 16, 14, 17), (9, 18)(11, 17, 12, 14)(13, 15, 16), (8, 18)(11, 13, 12, 16, 14), (8, 9, 18, 10)(11, 12, 17, 16)(13, 14, 15), (7, 10, 9, 8)(11, 16, 12, 15)(13, 17), (6, 9, 8, 7)(12, 16, 13, 17, 14, 15), (4, 5)(6, 7, 9, 8, 18)(11, 16, 13, 17, 15, 12, 14), (3, 5)(7, 18, 9)(11, 16, 14, 15)(12, 17, 13), (2, 4)(11, 15, 14, 16, 17)(12, 13), (2, 3)(6, 8, 10, 7, 9)(11, 12)(13, 17)(14, 16), (1, 4, 2, 5, 3)(6, 9)(11, 17, 14, 13, 16, 15, 12) orbits: { 1, 3, 5, 2, 4 }, { 6, 7, 18, 9, 8, 10 }, { 11, 13, 19, 16, 12, 14, 15, 17 }