[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 2 2 2 2 0 1 1 2 1 1 2 0 1 0 2 2 1 0 1 1 0 0 0 2] [0 1 1 0 1 1 2 1 0 1 2 1 2 1 1 2 2 0 2 0 2 0 2 0 0 2 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 0 1 1 2 1 2 2 2 0 0 2 0 0 1 1 1 0 1 0 2 1 2 1 2 0 2] [0 2 1 2 0 1 2 0 1 2 1 0 1 2 1 0 0 0 0 0 2 2 2 2 1 1 1] [0 2 2 0 2 2 1 2 0 2 1 2 1 2 2 1 1 0 1 0 1 0 1 0 0 1 0] [0 0 1 0 2 0 2 1 0 2 1 0 2 1 2 1 2 1 0 2 1 1 0 2 1 0 2] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 1 1 0 0 2 2 2 1 2 1 0 0 2 0 1 1 2 2 1 2 0 0 0 1 1] [0 2 2 2 2 1 1 1 1 1 2 0 0 0 0 1 2 1 0 2 0 0 2 1 2 1 0] [0 1 1 2 1 0 2 0 1 0 0 2 1 2 2 2 0 1 1 2 1 0 0 1 2 2 0] [0 1 2 0 0 1 1 2 0 0 0 1 1 2 0 0 1 1 2 2 0 1 2 2 1 2 2] [0 2 1 0 0 2 2 1 0 0 0 2 2 1 0 0 2 2 1 1 0 2 1 1 2 1 1] [0 1 1 1 1 2 2 2 2 2 1 0 0 0 0 2 1 2 0 1 0 0 1 2 1 2 0] [0 1 2 2 0 0 1 1 1 2 1 2 0 0 1 0 2 2 1 1 2 1 0 0 0 2 2] [0 0 2 0 1 0 1 2 0 1 2 0 1 2 1 2 1 2 0 1 2 2 0 1 2 0 1] [0 0 0 1 0 1 0 1 2 1 2 2 1 2 2 0 2 2 1 1 1 0 2 2 1 0 0] [0 0 2 1 1 1 1 0 2 2 1 2 2 1 0 2 0 1 1 2 0 2 2 0 0 0 1] [0 1 0 2 2 0 0 2 1 1 2 2 2 1 0 1 1 0 1 0 0 2 0 2 1 2 1] [0 0 2 2 1 2 1 1 1 0 0 1 0 0 2 2 2 0 2 0 1 2 1 2 1 0 1] [0 2 0 1 1 0 0 1 2 2 1 1 1 2 0 2 2 0 2 0 0 1 0 1 2 1 2] [0 2 2 1 2 0 1 0 2 0 0 1 2 1 1 1 0 2 2 1 2 0 0 2 1 1 0] [0 0 0 2 0 2 0 2 1 2 1 1 2 1 1 0 1 1 2 2 2 0 1 1 2 0 0] [0 1 0 1 2 2 0 1 2 0 0 0 1 2 1 1 2 1 0 2 2 2 1 0 0 2 1] [0 1 2 1 0 2 1 0 2 1 2 0 2 1 2 0 0 0 0 0 1 1 1 1 2 2 2] [0 2 0 2 1 1 0 2 1 0 0 0 2 1 2 2 1 2 0 1 1 1 2 0 0 1 2] Order of automorphism group: 24564384 The automorphism group has centre of order: 3 Number of regular subgroups: 60 Number of regular subgroups containing the center: 56 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 15> <27, 5> true <81, 15> <27, 5> true <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 11> <27, 5> false <81, 11> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 4> true <81, 13> <27, 4> true <81, 11> <27, 2> true <81, 11> <27, 2> true <81, 3> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 3> <27, 3> false <81, 3> <27, 3> false <81, 9> <27, 3> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 9> <27, 3> false <81, 3> <27, 3> false <81, 7> <27, 3> false <81, 8> <27, 3> false <81, 8> <27, 3> false <81, 7> <27, 3> false <81, 8> <27, 3> false <81, 8> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 14> <27, 5> false <81, 14> <27, 5> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 2 2 2 2 0 1 1 2 1 1 2 0 1 0 2 2 1 0 1 1 0 0 0 2] [0 1 2 0 1 1 1 2 0 1 0 1 1 2 1 0 1 2 0 2 0 2 0 2 2 0 2] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 0 1 1 2 1 2 2 2 0 0 2 0 0 1 1 1 0 1 0 2 1 2 1 2 0 2] [0 2 1 2 0 1 2 0 1 2 1 0 1 2 1 0 0 0 0 0 2 2 2 2 1 1 1] [0 2 1 0 2 2 2 1 0 2 0 2 2 1 2 0 2 1 0 1 0 1 0 1 1 0 1] [0 0 2 0 2 0 1 2 0 2 2 0 1 2 2 2 1 0 1 1 2 0 1 1 0 1 1] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 1 1 0 0 2 2 2 1 2 1 0 0 2 0 1 1 2 2 1 2 0 0 0 1 1] [0 2 0 2 2 1 0 2 1 1 0 0 2 1 0 2 1 0 1 1 1 2 0 0 1 2 2] [0 1 1 2 1 0 2 0 1 0 0 2 1 2 2 2 0 1 1 2 1 0 0 1 2 2 0] [0 1 1 0 0 1 2 1 0 0 2 1 2 1 0 2 2 2 1 0 2 2 1 0 2 1 0] [0 2 2 0 0 2 1 2 0 0 1 2 1 2 0 1 1 1 2 0 1 1 2 0 1 2 0] [0 1 1 1 1 2 2 2 2 2 1 0 0 0 0 2 1 2 0 1 0 0 1 2 1 2 0] [0 1 0 2 0 0 0 2 1 2 2 2 2 1 1 1 1 1 2 0 0 0 1 2 2 0 1] [0 0 1 0 1 0 2 1 0 1 1 0 2 1 1 1 2 0 2 2 1 0 2 2 0 2 2] [0 0 2 1 0 1 1 0 2 1 1 2 2 1 2 2 0 0 0 2 0 1 1 0 2 2 1] [0 0 0 1 1 1 0 1 2 2 2 2 1 2 0 0 2 0 2 1 1 1 0 2 2 1 0] [0 1 2 2 2 0 1 1 1 1 1 2 0 0 0 0 2 1 0 1 2 0 2 0 2 1 2] [0 0 0 2 1 2 0 2 1 0 1 1 2 1 2 0 1 2 0 2 2 1 2 1 0 1 0] [0 2 2 1 1 0 1 0 2 2 0 1 2 1 0 1 0 1 1 1 2 2 2 2 0 0 0] [0 2 0 1 2 0 0 1 2 0 1 1 1 2 1 2 2 1 0 0 0 2 1 1 0 2 2] [0 0 2 2 0 2 1 1 1 2 0 1 0 0 1 2 2 2 1 0 1 1 0 2 0 2 1] [0 1 2 1 2 2 1 0 2 0 2 0 2 1 1 0 0 2 2 0 1 0 0 1 1 1 2] [0 1 0 1 0 2 0 1 2 1 0 0 1 2 2 1 2 2 1 2 2 0 2 0 1 0 1] [0 2 2 2 1 1 1 1 1 0 2 0 0 0 2 1 2 0 2 2 0 2 1 1 1 0 0] Order of automorphism group: 472392 The automorphism group has centre of order: 3 Number of regular subgroups: 54 Number of regular subgroups containing the center: 50 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 11> <27, 2> true <81, 11> <27, 2> true <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 11> <27, 5> false <81, 12> <27, 5> false <81, 13> <27, 4> true <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 13> <27, 4> true <81, 13> <27, 4> true <81, 7> <27, 3> false <81, 12> <27, 5> false <81, 12> <27, 3> true <81, 13> <27, 4> true <81, 11> <27, 2> true <81, 13> <27, 4> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 3> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 5> false <81, 3> <27, 4> false <81, 3> <27, 2> false <81, 3> <27, 4> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 10> <27, 3> false <81, 13> <27, 5> false <81, 10> <27, 3> false <81, 8> <27, 3> false <81, 7> <27, 3> false <81, 14> <27, 5> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 2 2 2 0 2 1 1 0 1 2 1 0 2 1 2 2 0 1 1 1 2 0 0 1] [0 2 2 0 2 2 1 2 0 2 1 2 1 2 2 1 1 0 1 0 1 0 1 0 0 1 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 0 0 1 2 1 0 1 2 0 0 2 1 2 1 1 2 2 2 0 2 0 0 1 1 1 2] [0 2 0 2 0 1 0 2 1 2 2 0 2 1 1 1 1 0 0 2 0 2 2 1 1 1 0] [0 1 1 0 1 1 2 1 0 1 2 1 2 1 1 2 2 0 2 0 2 0 2 0 0 2 0] [0 1 2 0 0 1 1 2 0 0 0 1 1 2 0 0 1 1 2 2 0 1 2 2 1 2 2] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 0 1 0 0 0 1 2 1 2 1 1 2 2 0 2 0 0 2 1 1 1 0 2 2 1] [0 1 2 2 2 0 1 1 1 1 0 2 0 0 0 2 2 0 1 2 1 2 0 1 1 2 0] [0 1 0 2 1 0 0 2 1 0 1 2 2 1 2 0 1 1 1 1 2 0 0 0 2 2 2] [0 0 1 0 2 0 2 1 0 2 1 0 2 1 2 1 2 1 0 2 1 1 0 2 1 0 2] [0 0 2 0 1 0 1 2 0 1 2 0 1 2 1 2 1 2 0 1 2 2 0 1 2 0 1] [0 1 0 1 1 2 0 1 2 2 1 0 1 2 0 2 2 1 1 1 0 2 2 2 0 0 0] [0 0 2 2 0 2 1 1 1 2 2 1 0 0 1 1 2 1 2 1 0 0 1 0 2 0 2] [0 2 1 0 0 2 2 1 0 0 0 2 2 1 0 0 2 2 1 1 0 2 1 1 2 1 1] [0 0 1 1 1 1 2 2 2 2 1 2 0 0 0 2 1 0 2 2 0 1 0 0 2 1 1] [0 0 2 1 0 1 1 0 2 1 2 2 2 1 2 0 0 1 2 1 1 2 0 2 0 1 0] [0 2 1 2 2 1 2 0 1 1 0 0 1 2 0 2 0 1 0 1 1 0 2 0 2 1 2] [0 2 2 2 1 1 1 1 1 0 1 0 0 0 2 0 2 2 0 0 2 1 2 2 0 1 1] [0 2 1 1 2 0 2 2 2 0 0 1 0 0 1 1 1 1 0 1 2 2 1 2 0 2 0] [0 2 2 1 1 0 1 0 2 2 1 1 2 1 0 2 0 2 0 0 0 0 1 1 1 2 2] [0 1 1 2 0 0 2 0 1 2 2 2 1 2 1 1 0 2 1 0 0 1 0 2 0 2 1] [0 1 1 1 0 2 2 2 2 1 2 0 0 0 2 0 1 2 1 0 1 0 2 1 1 0 2] [0 1 2 1 2 2 1 0 2 0 0 0 2 1 1 1 0 0 1 2 2 1 2 0 2 0 1] [0 0 1 2 1 2 2 0 1 0 1 1 1 2 2 0 0 0 2 2 2 2 1 1 1 0 0] Order of automorphism group: 472392 The automorphism group has centre of order: 3 Number of regular subgroups: 54 Number of regular subgroups containing the center: 50 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 11> <27, 2> true <81, 11> <27, 2> true <81, 13> <27, 5> false <81, 12> <27, 5> false <81, 13> <27, 5> false <81, 11> <27, 5> false <81, 13> <27, 4> true <81, 3> <27, 2> false <81, 13> <27, 4> true <81, 13> <27, 4> true <81, 13> <27, 4> true <81, 11> <27, 2> true <81, 12> <27, 3> true <81, 3> <27, 2> false <81, 7> <27, 3> false <81, 12> <27, 5> false <81, 13> <27, 4> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 3> <27, 4> false <81, 3> <27, 3> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 7> <27, 3> false <81, 13> <27, 5> false <81, 3> <27, 2> false <81, 3> <27, 4> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 9> <27, 3> false <81, 14> <27, 5> false <81, 8> <27, 3> false <81, 7> <27, 3> false <81, 10> <27, 3> false <81, 10> <27, 3> false <81, 13> <27, 5> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 2 0 2 0 1 2 0 0 2 0 1 2 1 2 1 0 1 1 2 1 2 1 2 0 1] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 0 0 1 1 1 0 1 2 2 0 2 1 2 0 1 2 1 1 0 2 2 2 1 0 0 2] [0 2 1 1 1 2 2 2 2 2 0 2 0 0 0 0 1 0 2 1 0 1 0 1 2 1 1] [0 0 2 1 2 1 1 0 2 1 2 2 2 1 0 0 0 0 1 1 1 2 0 2 1 2 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 1 0 1 0 2 0 1 2 1 1 0 1 2 2 2 2 0 0 1 0 1 1 2 2 2 0] [0 0 0 2 2 2 0 2 1 1 0 1 2 1 0 2 1 2 2 0 1 1 1 2 0 0 1] [0 0 1 2 2 1 2 0 1 1 1 2 1 2 0 2 0 1 0 2 0 0 2 0 2 1 1] [0 1 2 0 1 1 1 2 0 2 0 1 1 2 0 0 1 2 0 2 0 0 1 2 1 2 2] [0 0 2 2 2 2 1 1 1 2 2 1 0 0 2 1 2 0 1 1 0 0 1 0 0 1 2] [0 2 0 1 2 0 0 1 2 0 2 1 1 2 1 0 2 2 2 2 1 0 0 0 1 1 1] [0 1 0 2 1 0 0 2 1 0 1 2 2 1 2 0 1 1 1 1 2 0 0 0 2 2 2] [0 1 1 0 0 0 2 1 0 0 2 2 2 1 0 1 2 2 1 0 0 2 1 2 2 1 1] [0 1 2 1 1 2 1 0 2 0 0 0 2 1 2 1 0 2 0 2 2 1 2 0 0 1 1] [0 2 0 2 0 1 0 2 1 2 2 0 2 1 1 1 1 0 0 2 0 2 2 1 1 1 0] [0 1 1 1 2 1 2 2 2 0 2 1 0 0 1 2 1 1 0 0 2 2 1 0 0 2 0] [0 0 1 1 0 0 2 2 2 1 1 0 0 0 2 1 1 2 1 2 1 0 2 2 1 0 2] [0 2 2 0 0 2 1 2 0 1 1 2 1 2 2 1 1 1 2 0 1 2 0 0 0 1 0] [0 1 2 2 1 0 1 1 1 1 0 2 0 0 1 2 2 2 0 2 1 2 0 1 2 0 0] [0 2 1 2 0 0 2 0 1 2 0 1 1 2 1 1 0 2 1 1 2 1 0 2 0 2 0] [0 1 1 2 1 2 2 0 1 0 2 0 1 2 2 0 0 0 2 0 1 2 1 1 1 0 2] [0 2 2 1 0 0 1 0 2 2 1 1 2 1 1 2 0 1 2 0 0 0 1 1 2 0 2] [0 0 1 0 1 2 2 1 0 1 1 1 2 1 1 0 2 0 2 2 2 0 2 1 0 2 0] [0 2 1 0 2 1 2 1 0 2 0 0 2 1 2 2 2 1 0 1 1 1 0 0 1 0 2] [0 2 2 2 0 1 1 1 1 0 1 0 0 0 0 0 2 1 2 0 2 1 2 2 1 2 1] Order of automorphism group: 39366 The automorphism group has centre of order: 3 Number of regular subgroups: 8 Number of regular subgroups containing the center: 8 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 11> <27, 2> true <81, 11> <27, 2> true [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 2 1 0 1 2 2 2 2 1 0 1 2 1 1 2 2 0 0 1 0 0 0 2 1 1] [0 0 0 2 1 2 0 0 2 1 1 2 1 2 0 2 1 1 2 0 1 2 1 2 0 1 0] [0 2 2 1 2 2 0 1 0 2 0 0 2 0 1 2 1 1 1 1 0 1 0 2 2 1 0] [0 0 1 1 0 0 0 2 0 2 1 2 2 1 0 2 2 0 1 1 1 2 2 1 1 0 2] [0 2 1 1 1 0 2 0 1 2 2 0 0 2 2 2 1 0 0 2 1 1 1 0 1 2 0] [0 1 2 2 0 0 1 2 0 1 0 1 1 2 1 2 1 0 0 2 2 1 2 2 0 0 1] [0 1 0 1 2 2 1 0 1 2 2 1 0 2 1 1 2 2 1 0 0 2 2 1 0 0 0] [0 1 2 0 1 0 2 1 2 0 2 0 2 1 0 1 2 0 1 2 0 2 1 2 0 1 1] [0 1 1 2 1 1 0 2 0 1 0 0 1 0 2 1 2 2 2 2 0 2 0 1 1 2 0] [0 0 1 2 2 0 2 2 1 1 2 1 2 0 1 0 1 0 2 0 0 0 1 1 2 1 2] [0 0 2 2 1 2 1 1 2 1 2 1 0 1 2 2 2 1 0 1 0 0 0 0 1 0 2] [0 0 0 1 1 1 1 1 0 2 2 2 1 1 2 0 0 0 2 0 0 1 2 2 2 2 1] [0 2 1 2 2 1 0 0 2 1 2 2 2 1 1 0 0 2 1 2 1 1 0 0 0 0 1] [0 2 2 0 0 2 0 2 1 0 2 2 1 2 1 0 0 1 0 1 0 2 1 1 1 2 1] [0 1 2 2 0 2 2 1 1 1 1 0 0 0 0 0 0 2 1 0 1 1 2 2 1 2 2] [0 2 1 1 1 1 1 2 2 2 0 1 0 0 0 0 0 2 0 1 2 2 1 2 0 1 2] [0 0 1 0 2 0 1 2 2 0 1 1 2 2 2 1 0 1 1 0 2 1 0 2 1 2 0] [0 2 2 0 1 1 2 1 0 0 1 1 2 2 2 0 1 2 2 1 1 0 2 1 0 0 0] [0 0 0 0 2 1 2 0 1 0 0 0 1 1 1 2 2 2 2 1 2 1 1 2 1 0 2] [0 2 0 2 0 1 1 1 1 1 0 2 2 2 0 1 2 0 1 1 2 0 1 0 2 2 0] [0 2 1 0 0 2 1 0 0 0 2 1 1 0 0 1 2 1 2 2 1 1 2 0 2 1 2] [0 1 1 0 1 2 0 2 1 0 0 2 0 1 2 2 1 2 1 0 2 0 2 0 2 1 1] [0 1 2 1 2 0 0 1 1 2 1 2 1 0 2 1 0 1 2 2 2 0 1 0 0 0 2] [0 1 0 1 0 2 2 0 2 2 0 1 2 1 0 0 1 1 2 2 2 0 0 1 1 2 1] [0 1 0 0 2 1 1 1 2 0 1 2 0 0 1 2 1 0 0 2 1 2 0 1 2 2 2] [0 2 0 2 2 0 2 0 0 1 1 0 0 1 2 1 0 1 0 1 2 2 2 1 2 1 1] Order of automorphism group: 11664 The automorphism group has centre of order: 3 Number of regular subgroups: 10 Number of regular subgroups containing the center: 10 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 12> <27, 3> true <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 15> <27, 5> true <81, 12> <27, 5> false <81, 15> <27, 5> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true [0 0 0 0 0 0 0 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 1 1 0 2 2 2 1 1 0 2 0 1 2 1 2 1 2 0 2 0 1 2] [0 2 1 2 1 0 0 2 0 1 0 1 1 1 1 1 2 2 0 1 2 2 0 2 0 0 2] [0 1 2 2 2 2 0 1 1 1 2 1 0 1 2 0 0 2 1 0 2 0 2 1 0 1 0] [0 0 0 2 0 2 2 2 1 1 1 2 1 0 1 2 2 0 2 1 1 1 2 0 0 1 0] [0 0 1 2 0 0 1 2 1 1 0 0 2 2 2 0 1 1 1 0 2 1 1 0 2 2 2] [0 1 1 0 2 2 1 2 2 0 0 2 2 0 1 1 0 2 1 2 1 1 0 1 2 0 0] [0 1 2 1 1 0 0 1 0 2 2 1 2 2 2 2 1 0 2 1 1 1 0 0 2 0 0] [0 1 0 1 2 0 1 0 1 2 1 1 2 0 1 1 2 0 0 0 2 0 2 2 2 2 1] [0 2 1 1 1 1 0 2 2 2 1 2 0 2 1 0 0 1 2 0 1 0 1 2 0 2 0] [0 1 2 2 2 1 2 0 0 1 1 2 1 1 0 0 1 1 0 2 0 1 0 2 2 2 0] [0 1 0 1 2 2 2 2 0 2 1 0 0 2 0 1 0 1 1 1 2 2 0 0 1 1 2] [0 2 2 0 0 1 0 1 0 0 1 2 2 0 1 0 1 0 1 1 2 2 2 1 1 2 2] [0 2 2 1 1 2 2 1 1 2 0 0 1 0 2 1 0 0 0 2 0 1 1 1 0 2 2] [0 2 2 2 1 0 1 1 2 1 1 0 0 0 0 2 2 2 1 2 1 0 0 0 1 2 1] [0 1 1 0 1 1 2 2 1 0 2 0 1 2 0 2 1 0 1 2 2 0 2 2 0 0 1] [0 0 2 0 0 0 2 1 2 0 2 1 0 2 1 1 2 1 0 2 2 1 1 2 1 1 0] [0 0 1 2 2 1 0 1 2 1 2 0 2 0 0 1 0 0 2 1 0 2 1 2 2 1 1] [0 0 2 1 0 2 0 0 2 2 0 2 1 1 0 2 2 1 1 1 2 0 1 1 2 0 1] [0 2 0 0 1 2 2 2 2 0 1 1 2 1 2 0 1 2 0 1 0 0 1 0 2 1 1] [0 2 0 2 0 1 2 0 0 1 0 1 2 2 2 1 0 1 2 2 1 0 2 1 1 0 1] [0 1 0 0 2 1 0 0 1 0 0 0 0 1 2 2 2 2 2 1 1 1 1 2 1 2 2] [0 1 0 2 1 2 1 0 2 1 2 2 0 2 1 2 1 0 0 0 0 2 1 1 1 0 2] [0 0 1 1 2 0 2 1 1 2 0 2 0 1 1 0 1 2 2 2 0 2 2 0 1 0 1] [0 2 2 0 1 0 1 0 1 0 2 2 1 1 0 1 0 1 2 0 1 2 2 0 2 1 2] [0 2 1 1 0 1 1 2 0 2 2 0 2 1 0 2 2 2 0 0 0 1 2 1 1 1 0] [0 0 1 0 2 2 1 1 0 0 1 1 1 2 2 2 2 1 2 0 0 2 0 1 0 2 1] Order of automorphism group: 11664 The automorphism group has centre of order: 3 Number of regular subgroups: 10 Number of regular subgroups containing the center: 10 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 12> <27, 3> true <81, 12> <27, 5> false <81, 15> <27, 5> true <81, 12> <27, 3> true <81, 12> <27, 5> false <81, 15> <27, 5> true <81, 12> <27, 5> false <81, 12> <27, 3> true <81, 12> <27, 3> true <81, 12> <27, 3> true [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 2 2 2 2 2 1 1 0 1 1 1 0 2 0 2 2 1 1 1 1 0 0 0 2] [0 1 1 0 1 1 2 1 0 1 0 1 2 1 1 0 2 2 0 2 0 2 0 2 2 0 2] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 0 0 1 2 1 2 1 2 0 0 2 0 2 1 1 1 0 2 0 2 1 0 1 2 1 2] [0 2 0 2 0 1 2 2 1 2 2 0 1 1 1 1 0 0 0 0 0 2 2 2 1 1 1] [0 1 2 0 1 1 1 2 0 1 2 1 1 2 1 2 1 0 2 0 2 0 2 0 0 2 0] [0 0 1 0 2 0 2 1 0 2 2 0 2 1 2 2 2 0 1 1 2 0 1 1 0 1 1] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 0 1 0 0 2 1 2 1 2 1 0 2 2 0 1 1 0 2 1 2 1 0 0 2 1] [0 2 2 2 2 1 0 1 1 1 0 0 2 0 0 2 1 0 1 2 1 2 0 1 1 2 0] [0 1 0 2 1 0 2 2 1 0 1 2 1 1 2 0 0 1 1 2 2 0 0 1 2 2 0] [0 0 2 0 2 0 1 2 0 2 1 0 1 2 2 1 1 1 0 2 1 1 0 2 1 0 2] [0 2 1 0 0 2 2 1 0 0 1 2 2 1 0 1 2 1 2 0 1 1 2 0 1 2 0] [0 1 0 1 1 2 2 1 2 2 1 0 0 2 0 2 1 2 1 1 0 0 2 2 1 0 0] [0 1 2 2 0 0 0 1 1 2 2 2 2 0 1 1 1 1 2 1 0 0 1 0 2 0 2] [0 2 2 0 0 2 1 2 0 0 0 2 1 2 0 0 1 2 1 1 0 2 1 1 2 1 1] [0 0 1 1 1 1 1 2 2 2 1 2 2 0 0 2 0 0 0 2 0 1 1 0 2 2 1] [0 0 2 1 1 1 0 0 2 2 2 2 1 1 0 0 2 1 2 1 1 2 0 2 0 1 0] [0 2 1 2 2 1 1 0 1 1 1 0 0 2 0 0 2 1 0 1 2 0 2 0 2 1 2] [0 0 2 2 1 2 0 1 1 0 1 1 2 0 2 0 1 2 0 0 2 1 2 2 0 1 1] [0 2 1 1 2 0 1 2 2 0 0 1 2 0 1 1 0 1 1 1 2 2 2 2 0 0 0] [0 2 2 1 2 0 0 0 2 0 1 1 1 1 1 2 2 2 0 0 0 0 1 1 1 2 2] [0 1 1 2 0 0 1 0 1 2 0 2 0 2 1 2 2 2 1 0 1 1 0 2 0 2 1] [0 1 1 1 0 2 1 2 2 1 2 0 2 0 2 0 0 2 2 0 1 0 0 1 1 1 2] [0 1 2 1 0 2 0 0 2 1 0 0 1 1 2 1 2 0 1 2 2 1 2 0 2 0 1] [0 0 1 2 1 2 1 0 1 0 2 1 0 2 2 1 2 0 2 2 0 2 1 1 1 0 0] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 11 Number of regular subgroups containing the center: 9 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 11> <27, 2> true <81, 3> <27, 2> false <81, 13> <27, 4> true <81, 11> <27, 2> true <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 3> <27, 2> false <81, 13> <27, 4> true <81, 3> <27, 4> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 1 1 1 1 2 2 0 2 2 2 0 1 0 1 1 2 2 2 2 0 0 0 1] [0 2 2 0 2 2 1 2 0 2 0 2 1 2 2 0 1 1 0 1 0 1 0 1 1 0 1] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 0 0 2 1 2 1 2 1 0 0 1 0 1 2 2 2 0 1 0 1 2 0 2 1 2 1] [0 1 0 1 0 2 1 1 2 1 1 0 2 2 2 2 0 0 0 0 0 1 1 1 2 2 2] [0 2 1 0 2 2 2 1 0 2 1 2 2 1 2 1 2 0 1 0 1 0 1 0 0 1 0] [0 0 2 0 1 0 1 2 0 1 1 0 1 2 1 1 1 0 2 2 1 0 2 2 0 2 2] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 1 0 2 0 0 1 2 1 2 1 2 0 1 1 0 2 2 0 1 2 1 2 0 0 1 2] [0 1 1 1 1 2 0 2 2 2 0 0 1 0 0 1 2 0 2 1 2 1 0 2 2 1 0] [0 2 0 1 2 0 1 1 2 0 2 1 2 2 1 0 0 2 2 1 1 0 0 2 1 1 0] [0 0 1 0 1 0 2 1 0 1 2 0 2 1 1 2 2 2 0 1 2 2 0 1 2 0 1] [0 1 2 0 0 1 1 2 0 0 2 1 1 2 0 2 1 2 1 0 2 2 1 0 2 1 0] [0 2 0 2 2 1 1 2 1 1 2 0 0 1 0 1 2 1 2 2 0 0 1 1 2 0 0] [0 2 1 1 0 0 0 2 2 1 1 1 1 0 2 2 2 2 1 2 0 0 2 0 1 0 1] [0 1 1 0 0 1 2 1 0 0 0 1 2 1 0 0 2 1 2 2 0 1 2 2 1 2 2] [0 0 2 2 2 2 2 1 1 1 2 1 1 0 0 1 0 0 0 1 0 2 2 0 1 1 2] [0 0 1 2 2 2 0 0 1 1 1 1 2 2 0 0 1 2 1 2 2 1 0 1 0 2 0] [0 1 2 1 1 2 2 0 2 2 2 0 0 1 0 0 1 2 0 2 1 0 1 0 1 2 1] [0 0 1 1 2 1 0 2 2 0 2 2 1 0 1 0 2 1 0 0 1 2 1 1 0 2 2] [0 1 2 2 1 0 2 1 1 0 0 2 1 0 2 2 0 2 2 2 1 1 1 1 0 0 0] [0 1 1 2 1 0 0 0 1 0 2 2 2 2 2 1 1 1 0 0 0 0 2 2 2 1 1] [0 2 2 1 0 0 2 0 2 1 0 1 0 1 2 1 1 1 2 0 2 2 0 1 0 1 2] [0 2 2 2 0 1 2 1 1 2 1 0 1 0 1 0 0 1 1 0 2 0 0 2 2 2 1] [0 2 1 2 0 1 0 0 1 2 0 0 2 2 1 2 1 0 2 1 1 2 1 0 1 0 2] [0 0 2 1 2 1 2 0 2 0 1 2 0 1 1 2 1 0 1 1 0 1 2 2 2 0 0] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 11 Number of regular subgroups containing the center: 9 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 11> <27, 2> true <81, 3> <27, 2> false <81, 13> <27, 4> true <81, 11> <27, 2> true <81, 13> <27, 4> true <81, 3> <27, 4> false <81, 3> <27, 2> false <81, 3> <27, 4> false <81, 3> <27, 4> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 2 2 0 0 1 1 0 0 2 2 0 0 0 1 1 1 2 1 2 1 1 2 2 1 2] [0 1 1 0 1 2 1 0 0 0 1 2 1 2 2 0 2 1 1 2 0 1 0 0 2 2 2] [0 1 0 0 2 0 0 0 2 1 1 0 0 2 1 1 0 2 2 1 1 1 2 2 1 2 2] [0 0 0 1 0 2 1 2 2 2 1 0 2 2 2 1 1 2 1 1 0 2 1 0 0 1 0] [0 1 2 0 1 1 2 0 2 2 1 1 2 0 0 2 1 1 1 0 2 1 2 2 0 0 0] [0 2 1 0 0 2 1 0 2 1 2 2 1 1 0 1 2 0 0 0 1 2 2 2 0 1 1] [0 2 0 0 1 0 0 0 1 2 2 0 0 1 2 2 0 1 1 2 2 2 1 1 2 1 1] [0 1 2 1 1 0 0 2 1 2 2 1 1 2 1 1 2 0 2 0 0 0 0 2 2 1 0] [0 2 1 2 0 1 0 1 2 0 1 0 2 1 1 1 2 1 2 2 2 0 0 1 0 2 0] [0 1 2 2 2 0 1 1 2 1 0 2 0 2 1 2 1 0 1 2 0 2 0 1 0 0 1] [0 2 2 0 0 1 2 0 1 0 2 1 2 2 1 0 1 0 0 1 0 2 1 1 1 2 2] [0 0 1 0 2 2 1 0 1 2 0 2 1 0 1 2 2 2 2 1 2 0 1 1 1 0 0] [0 2 1 1 0 1 2 2 1 2 0 2 0 0 0 1 0 2 1 2 0 1 0 2 1 2 1] [0 0 0 2 2 2 2 1 0 2 2 1 1 1 1 0 0 0 1 2 1 1 1 2 0 2 0] [0 1 1 2 1 1 0 1 0 2 0 0 2 2 0 0 2 2 0 1 1 2 1 2 2 0 1] [0 0 2 0 2 1 2 0 0 1 0 1 2 1 2 1 1 2 2 2 1 0 0 0 2 1 1] [0 2 0 1 1 2 1 2 0 1 0 0 2 0 1 0 1 0 2 0 2 1 2 1 2 2 1] [0 1 0 1 2 2 1 2 1 0 2 0 2 1 0 2 1 1 0 2 1 0 0 2 1 0 2] [0 2 0 2 0 2 2 1 1 1 1 1 1 2 0 2 0 1 2 1 0 0 2 0 2 0 1] [0 0 1 2 2 1 0 1 1 1 2 0 2 0 2 2 2 0 1 0 0 1 2 0 1 1 2] [0 2 2 2 1 0 1 1 1 2 1 2 0 1 2 0 1 2 0 0 1 0 2 0 1 2 0] [0 0 2 1 2 0 0 2 2 1 1 1 1 0 0 0 2 1 0 2 2 2 1 0 1 2 1] [0 2 2 1 0 0 0 2 0 0 0 1 1 1 2 2 2 2 1 1 1 1 2 1 0 0 2] [0 1 0 2 1 2 2 1 2 0 0 1 1 0 2 1 0 2 0 0 2 2 0 1 1 1 2] [0 1 1 1 1 1 2 2 2 1 2 2 0 1 2 0 0 0 2 1 2 0 1 0 0 0 2] [0 0 1 1 2 1 2 2 0 0 1 2 0 2 1 2 0 1 0 0 1 2 2 1 2 1 0] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 23 Number of regular subgroups containing the center: 21 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 13> <27, 4> true <81, 11> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 13> <27, 5> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 4> true [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 2 2 2 2 2 1 1 1 1 1 1 0 0 0 0 2 2 1 2 1 1 0 0 0 2] [0 1 2 0 1 1 1 2 0 1 2 1 1 2 1 2 1 0 2 0 2 0 2 0 0 2 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 0 2 1 2 1 2 0 2 0 0 2 0 1 1 1 1 0 0 0 2 1 1 1 2 2 2] [0 2 2 2 0 1 2 1 1 2 0 0 1 0 1 2 0 0 0 0 1 2 2 2 1 1 1] [0 0 1 0 0 0 2 1 0 0 2 0 2 1 0 2 2 1 2 1 2 1 2 1 1 2 1] [0 0 2 0 2 0 1 2 0 2 1 0 1 2 2 1 1 1 0 2 1 1 0 2 1 0 2] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 2 1 0 0 2 0 2 1 2 1 0 1 2 0 1 1 1 2 1 2 2 0 0 0 1] [0 2 0 2 2 1 1 2 1 1 2 0 0 1 0 1 2 1 0 1 0 0 2 0 2 1 2] [0 1 2 2 1 0 2 1 1 0 2 2 1 0 2 1 0 1 1 2 0 0 0 1 2 2 0] [0 2 1 0 1 2 2 1 0 1 1 2 2 1 1 1 2 2 0 0 1 2 0 0 2 0 0] [0 2 2 0 0 2 1 2 0 0 0 2 1 2 0 0 1 2 1 1 0 2 1 1 2 1 1] [0 1 2 1 1 2 2 0 2 2 1 0 0 1 0 2 1 2 2 1 0 0 0 2 1 1 0] [0 1 0 2 0 0 1 2 1 2 1 2 0 1 1 0 2 2 1 0 2 1 0 2 0 2 1] [0 1 1 0 2 1 2 1 0 2 0 1 2 1 2 0 2 0 1 2 0 0 1 2 0 1 2] [0 0 1 1 2 1 0 2 2 0 2 2 1 0 1 0 2 2 1 1 1 0 2 2 1 0 0] [0 0 0 1 1 1 1 1 2 2 1 2 2 2 0 2 0 0 1 2 0 1 2 0 2 0 1] [0 0 1 2 2 2 0 0 1 1 2 1 2 2 0 1 1 0 1 0 0 2 0 2 1 2 1] [0 0 0 2 1 2 1 2 1 0 0 1 0 1 2 2 2 0 2 2 1 2 1 1 1 0 0] [0 2 1 1 0 0 0 2 2 1 1 1 1 0 2 2 2 0 2 0 0 1 0 1 2 1 2] [0 2 0 1 2 0 1 1 2 0 0 1 2 2 1 1 0 1 2 1 2 2 0 2 0 1 0] [0 2 1 2 0 1 0 0 1 2 1 0 2 2 1 0 1 1 2 2 2 0 1 1 2 0 0] [0 1 1 1 1 2 0 2 2 2 0 0 1 0 0 1 2 1 0 2 2 2 1 0 0 2 1] [0 1 0 1 0 2 1 1 2 1 2 0 2 2 2 0 0 2 0 0 1 0 1 1 1 2 2] [0 1 1 2 1 0 0 0 1 0 0 2 2 2 2 2 1 2 0 1 1 1 2 0 0 1 2] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 23 Number of regular subgroups containing the center: 21 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 12> <27, 5> false <81, 13> <27, 4> true <81, 11> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 13> <27, 5> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 4> true <81, 3> <27, 4> false <81, 3> <27, 4> false <81, 13> <27, 5> false <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 3> <27, 4> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 2 0 2 1 1 0 2 0 0 2 1 1 1 0 2 2 0 2 1 1 0 2 0 1 2] [0 2 0 1 1 0 0 0 1 2 1 2 1 1 1 1 2 1 2 0 2 2 2 2 0 0 0] [0 0 1 0 0 1 0 2 1 0 1 0 2 1 0 2 1 2 1 0 2 1 2 2 1 2 2] [0 2 0 0 1 1 2 0 0 0 2 1 2 1 2 0 0 1 2 1 2 1 0 1 2 2 1] [0 0 0 1 0 1 1 2 1 2 0 1 2 2 2 0 2 1 1 2 0 0 1 2 2 1 0] [0 1 0 0 2 2 1 2 0 0 1 2 0 2 1 2 0 1 1 2 0 2 2 1 1 0 1] [0 0 0 2 2 2 2 0 2 1 2 1 1 1 1 2 1 2 1 0 0 0 1 1 0 2 0] [0 2 1 1 1 1 0 2 2 2 2 2 0 2 1 0 0 0 0 0 1 0 1 1 1 2 2] [0 0 2 0 0 2 0 1 2 0 2 0 1 2 0 1 2 1 2 0 1 2 1 1 2 1 1] [0 1 0 1 2 2 2 0 1 2 2 0 2 0 0 1 2 0 0 1 0 1 2 1 1 1 2] [0 2 1 0 1 2 2 2 1 0 0 1 1 2 2 2 1 0 0 1 1 2 2 0 0 1 0] [0 2 1 2 0 1 1 1 0 1 2 2 0 0 0 0 2 2 1 1 2 2 2 1 0 1 0] [0 0 1 1 0 2 1 1 2 2 1 1 1 0 2 2 0 0 2 2 2 1 0 1 0 0 2] [0 1 1 0 2 0 1 1 1 0 2 2 2 0 1 1 1 0 2 2 2 0 1 0 2 2 0] [0 0 1 2 2 0 2 2 0 1 0 1 0 2 1 1 2 1 2 0 2 1 0 0 1 1 2] [0 2 2 1 1 2 0 1 0 2 0 2 2 0 1 2 1 2 1 0 0 1 0 0 2 1 1] [0 1 0 2 1 1 0 0 2 1 0 0 0 0 2 2 1 0 2 2 2 2 1 2 1 1 1] [0 1 1 1 2 0 2 2 2 2 0 0 1 1 0 0 0 2 1 1 2 2 1 0 2 0 1] [0 2 2 0 1 0 2 1 2 0 1 1 0 0 2 1 2 2 1 1 0 0 1 2 1 0 2] [0 2 2 2 0 2 1 0 1 1 0 2 2 1 0 2 0 1 2 1 1 0 1 0 1 0 2] [0 0 2 1 0 0 1 0 0 2 2 1 0 1 2 1 1 2 0 2 1 2 2 0 1 2 1] [0 0 2 2 2 1 2 1 1 1 1 1 2 0 1 0 0 0 0 0 1 2 2 2 2 0 1] [0 1 1 2 1 2 0 2 0 1 1 0 2 1 2 1 2 2 0 2 1 0 0 1 2 0 0] [0 1 2 1 2 1 2 1 0 2 1 0 0 2 0 2 1 1 2 1 1 0 0 2 0 2 0] [0 2 0 2 0 0 1 2 2 1 1 2 1 2 0 1 1 0 0 1 0 1 0 2 2 2 1] [0 1 2 2 1 0 0 1 1 1 2 0 1 2 2 0 0 1 1 2 0 1 2 0 0 2 2] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 11 Number of regular subgroups containing the center: 9 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 11> <27, 2> true <81, 3> <27, 2> false <81, 12> <27, 3> true <81, 11> <27, 2> true <81, 12> <27, 3> true <81, 3> <27, 3> false <81, 3> <27, 2> false <81, 3> <27, 3> false <81, 3> <27, 3> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 2 1 0 1 2 2 0 1 0 0 1 2 2 2 0 1 1 0 1 2 2 0 1 0 2 1] [0 1 0 2 2 0 0 0 2 1 2 1 2 2 2 2 1 2 1 0 1 1 1 1 0 0 0] [0 0 2 0 0 2 0 1 2 0 2 0 1 2 0 1 2 1 2 0 1 2 1 1 2 1 1] [0 1 0 0 2 2 1 0 0 0 1 2 1 2 1 0 0 2 1 2 1 2 0 2 1 1 2] [0 0 0 2 0 2 2 1 2 1 0 2 1 1 1 0 1 2 2 1 0 0 2 1 1 2 0] [0 2 0 0 1 1 2 1 0 0 2 1 0 1 2 1 0 2 2 1 0 1 1 2 2 0 2] [0 0 0 1 1 1 1 0 1 2 1 2 2 2 2 1 2 1 2 0 0 0 2 2 0 1 0] [0 1 2 2 2 2 0 1 1 1 1 1 0 1 2 0 0 0 0 0 2 0 2 2 2 1 1] [0 0 1 0 0 1 0 2 1 0 1 0 2 1 0 2 1 2 1 0 2 1 2 2 1 2 2] [0 2 0 2 1 1 1 0 2 1 1 0 1 0 0 2 1 0 0 2 0 2 1 2 2 2 1] [0 1 2 0 2 1 1 1 2 0 0 2 2 1 1 1 2 0 0 2 2 1 1 0 0 2 0] [0 1 2 1 0 2 2 2 0 2 1 1 0 0 0 0 1 1 2 2 1 1 1 2 0 2 0] [0 0 2 2 0 1 2 2 1 1 2 2 2 0 1 1 0 0 1 1 1 2 0 2 0 0 1] [0 2 2 0 1 0 2 2 2 0 1 1 1 0 2 2 2 0 1 1 1 0 2 0 1 1 0] [0 0 2 1 1 0 1 1 0 2 0 2 0 1 2 2 1 2 1 0 1 2 0 0 2 2 1] [0 1 1 2 2 1 0 2 0 1 0 1 1 0 2 1 2 1 2 0 0 2 0 0 1 2 2] [0 2 0 1 2 2 0 0 1 2 0 0 0 0 1 1 2 0 1 1 1 1 2 1 2 2 2] [0 2 2 2 1 0 1 1 1 1 0 0 2 2 0 0 0 1 2 2 1 1 2 0 1 0 2] [0 1 1 0 2 0 1 2 1 0 2 2 0 0 1 2 1 1 2 2 0 0 2 1 2 0 1] [0 1 1 1 0 1 2 0 2 2 0 1 1 2 0 1 0 2 1 2 2 0 2 0 2 0 1] [0 0 1 2 0 0 2 0 0 1 1 2 0 2 1 2 2 1 0 1 2 1 1 0 2 1 2] [0 0 1 1 1 2 1 2 2 2 2 2 1 0 2 0 0 0 0 0 2 1 1 1 1 0 2] [0 2 2 1 2 1 0 1 0 2 2 0 1 2 1 2 1 1 0 1 2 0 0 2 1 0 0] [0 2 1 2 1 2 1 2 0 1 2 0 0 1 0 1 2 2 1 2 2 0 0 1 0 1 0] [0 1 0 1 0 0 2 1 1 2 2 1 2 1 0 2 2 0 0 2 0 2 0 1 1 1 2] [0 2 1 1 2 0 0 2 2 2 1 0 2 1 1 0 0 2 2 1 0 2 1 0 0 1 1] Order of automorphism group: 8748 The automorphism group has centre of order: 3 Number of regular subgroups: 11 Number of regular subgroups containing the center: 9 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 11> <27, 2> true <81, 3> <27, 2> false <81, 12> <27, 3> true <81, 11> <27, 2> true <81, 12> <27, 3> true <81, 3> <27, 3> false <81, 3> <27, 2> false <81, 3> <27, 3> false <81, 3> <27, 3> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 2 1 0 2 0 1 1 2 2 1 2 2 1 0 0 0 0 2 2 1 1 2 0 1] [0 2 2 2 2 0 1 1 1 1 0 1 0 0 0 1 2 0 1 1 2 2 0 2 1 2 0] [0 1 2 2 0 2 1 1 1 2 2 0 0 0 1 0 2 1 2 0 1 0 1 1 2 0 2] [0 1 2 1 2 0 2 1 0 2 1 1 2 1 2 2 0 1 0 0 2 1 0 0 1 0 2] [0 2 0 1 1 1 0 1 2 2 0 2 1 2 1 1 2 2 1 0 1 2 0 0 0 0 2] [0 2 1 1 1 1 2 2 2 2 1 0 0 0 0 0 1 0 2 0 2 1 0 2 2 1 1] [0 1 1 1 2 0 2 2 2 0 0 2 0 0 1 2 1 1 0 2 1 2 1 1 0 2 0] [0 0 1 1 0 2 2 2 2 1 2 1 0 0 2 1 1 2 1 1 0 0 2 0 1 0 2] [0 2 0 2 2 0 1 0 2 1 1 0 2 1 0 1 1 2 2 2 0 1 1 1 0 0 2] [0 0 0 1 0 2 0 1 2 1 1 0 1 2 0 2 2 1 0 1 2 1 2 1 2 2 0] [0 1 2 0 2 2 1 2 0 1 1 2 1 2 1 1 1 2 0 0 0 0 0 2 2 1 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 2 1 0 1 2 0 2 1 2 0 1 2 1 0 2 2 2 0 0 0 0 1 1 1 2 1] [0 2 2 0 1 0 1 2 0 0 2 0 1 2 0 2 1 1 2 1 1 2 2 0 1 0 1] [0 0 2 2 1 1 1 1 1 0 1 2 0 0 2 2 2 2 0 2 0 1 2 0 0 1 1] [0 1 1 0 2 1 0 2 1 0 2 0 2 1 1 1 2 0 1 2 2 1 2 0 2 0 0] [0 0 0 2 1 1 1 0 2 0 2 1 2 1 2 2 1 1 1 0 1 0 0 2 2 2 0] [0 0 2 0 0 1 1 2 0 2 0 1 1 2 2 0 1 0 1 2 2 1 1 1 0 2 2] [0 1 1 2 0 1 2 0 1 0 0 0 1 2 1 2 0 2 2 1 0 1 0 2 1 2 2] [0 0 2 1 0 2 2 1 0 0 0 0 2 1 0 1 0 2 1 2 1 2 1 2 2 1 1] [0 0 1 0 0 0 0 2 1 1 1 2 2 1 2 0 2 1 2 1 1 2 0 2 0 1 2] [0 2 1 2 2 2 2 0 1 2 1 1 1 2 0 0 0 1 1 2 1 0 2 0 0 1 0] [0 1 0 2 0 2 1 0 2 2 0 2 2 1 1 0 1 0 0 1 2 2 2 0 1 1 1] [0 2 2 1 1 1 2 1 0 1 2 2 2 1 1 0 0 0 2 1 0 0 2 1 0 2 0] [0 1 0 1 2 0 0 1 2 0 2 1 1 2 2 0 2 0 2 2 0 0 1 2 1 1 1] Order of automorphism group: 1458 The automorphism group has centre of order: 3 Number of regular subgroups: 8 Number of regular subgroups containing the center: 8 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 11> <27, 2> true <81, 11> <27, 2> true [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 2 2 1 2 0 0 1 0 1 2 1 2 2 2 2 1 2 0 0 1 1 1 0] [0 1 2 2 0 2 1 1 1 1 2 0 0 0 2 0 2 2 1 0 1 0 2 1 1 0 2] [0 0 2 2 1 1 1 1 1 2 1 2 0 0 0 2 2 0 2 2 0 1 0 0 2 1 1] [0 2 0 2 1 2 1 0 2 1 0 2 2 1 0 0 1 2 2 1 0 0 1 1 0 2 1] [0 0 1 2 2 1 0 1 2 1 0 1 1 2 0 0 0 1 0 2 2 0 2 1 2 1 2] [0 0 1 1 1 2 2 2 2 0 2 1 0 0 2 1 1 2 0 1 0 1 2 0 0 1 2] [0 2 1 1 2 1 2 2 2 1 1 0 0 0 0 0 1 0 1 0 2 2 0 2 1 2 1] [0 1 1 1 0 0 2 2 2 2 0 2 0 0 1 2 1 1 2 2 1 0 1 1 2 0 0] [0 0 1 0 2 1 0 2 1 1 2 2 2 1 2 0 2 1 2 1 1 1 0 2 0 0 0] [0 1 1 2 1 2 0 1 2 0 1 2 1 2 2 1 0 0 2 0 0 2 1 2 1 0 0] [0 2 2 0 2 2 2 0 1 2 1 1 1 2 2 0 1 0 1 2 1 0 1 0 0 1 0] [0 2 0 0 1 2 0 0 0 1 2 2 0 0 1 2 0 1 1 2 2 1 1 2 1 1 2] [0 1 0 0 2 1 0 0 0 2 1 1 0 0 2 1 0 2 2 1 1 2 2 1 2 2 1] [0 1 2 1 2 0 2 1 0 0 1 2 2 1 0 0 0 2 1 1 2 1 1 0 2 0 2] [0 0 2 0 1 0 2 0 1 1 2 2 1 2 1 1 1 2 0 0 2 2 0 1 2 0 1] [0 2 2 2 2 0 1 1 1 0 0 1 0 0 1 1 2 1 0 1 2 2 1 2 0 2 0] [0 0 2 1 0 2 2 1 0 1 0 1 2 1 1 2 0 0 2 0 1 2 2 2 0 1 1] [0 1 1 0 1 2 0 2 1 0 0 0 2 1 1 1 2 0 1 2 2 0 2 0 2 2 1] [0 1 2 0 0 1 2 0 1 0 0 0 1 2 0 2 1 1 2 1 0 1 2 2 1 2 2] [0 1 0 1 1 0 1 2 0 2 2 1 1 2 0 0 2 1 1 2 0 2 2 2 0 0 1] [0 1 0 2 2 1 1 0 2 2 2 1 2 1 1 2 1 0 0 0 2 1 2 0 1 0 0] [0 2 2 1 1 1 2 1 0 2 2 0 2 1 2 1 0 1 0 2 0 0 0 1 1 2 0] [0 2 0 1 0 1 1 2 0 1 0 2 1 2 2 1 2 0 0 0 1 1 1 0 2 2 2] [0 2 1 0 0 0 0 2 1 2 1 1 2 1 0 2 2 2 0 0 0 2 1 1 1 1 2] [0 0 0 2 0 0 1 0 2 0 1 0 2 1 2 1 1 1 1 2 1 2 0 2 2 1 2] [0 2 1 2 0 0 0 1 2 2 2 0 1 2 1 2 0 2 1 1 1 1 0 0 0 2 1] Order of automorphism group: 1458 The automorphism group has centre of order: 3 Number of regular subgroups: 8 Number of regular subgroups containing the center: 8 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 3> <27, 2> false <81, 11> <27, 2> true <81, 11> <27, 2> true [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 2 2 0 0 1 1 0 0 2 2 0 2 1 1 1 1 2 2 2 1 1 2 0 0 1] [0 0 2 2 1 1 1 0 2 2 2 0 1 0 0 0 2 1 0 1 2 0 1 1 2 1 2] [0 1 1 2 2 0 1 1 0 2 0 0 1 2 1 2 0 0 1 1 2 2 0 0 1 2 2] [0 0 0 1 0 1 1 2 2 2 1 2 2 2 0 1 0 2 1 2 0 2 1 0 1 1 0] [0 2 1 1 0 2 2 1 2 0 0 0 0 1 2 2 2 1 1 2 1 0 1 0 0 1 2] [0 1 2 2 0 2 0 0 1 2 0 1 2 0 2 1 0 0 2 0 1 1 1 2 1 1 2] [0 2 1 1 1 2 1 2 2 0 0 2 1 0 1 0 2 0 2 1 0 1 2 2 1 0 0] [0 2 1 0 2 0 1 2 1 2 2 0 2 1 0 2 0 1 2 0 0 1 2 1 0 1 1] [0 2 2 1 2 1 2 1 1 1 0 2 0 0 0 1 0 0 0 2 2 0 2 1 1 2 1] [0 1 0 1 2 0 2 2 0 2 2 2 1 1 2 0 1 1 0 0 1 0 1 2 1 2 0] [0 0 0 1 2 1 1 1 0 0 1 1 2 2 2 2 2 0 0 0 1 1 2 1 2 0 2] [0 2 0 2 2 0 0 0 1 0 1 2 1 0 1 0 1 2 1 2 1 2 2 1 0 1 2] [0 0 2 2 2 2 1 0 1 1 2 1 0 1 2 2 1 2 1 1 0 0 2 0 1 0 0] [0 1 2 0 1 0 2 2 2 1 1 0 2 2 0 1 1 0 1 1 1 0 2 2 0 0 2] [0 1 2 1 0 0 0 1 2 1 2 1 2 0 1 0 2 1 1 0 0 2 2 0 2 2 1] [0 1 2 1 1 1 0 1 1 0 2 0 1 1 0 2 0 2 2 2 1 2 0 2 2 0 0] [0 2 1 2 1 0 2 1 1 2 1 1 0 2 1 1 2 2 0 0 0 0 0 2 2 1 0] [0 1 1 0 2 1 2 0 2 1 1 2 0 1 1 0 0 2 2 0 2 1 1 0 2 0 2] [0 0 0 0 2 2 0 2 1 1 0 0 0 2 1 1 2 1 2 1 1 2 1 1 2 2 0] [0 0 0 1 1 2 2 1 1 2 1 0 2 0 2 0 1 2 2 1 2 1 0 0 0 2 1] [0 2 0 0 1 2 2 0 2 0 2 1 1 2 2 1 0 1 1 0 2 2 0 1 1 0 1] [0 1 2 0 0 2 0 2 0 0 1 2 2 1 1 2 2 2 0 1 2 0 0 1 1 1 1] [0 0 1 0 1 1 0 2 0 2 0 1 0 1 2 0 1 0 1 2 2 2 2 2 2 1 1] [0 2 1 0 0 2 1 2 0 1 2 1 1 0 0 1 1 2 0 2 1 1 0 0 2 2 2] [0 2 0 2 0 1 2 0 0 1 1 1 1 1 0 2 2 0 2 1 0 2 1 2 0 2 1] [0 1 1 2 1 1 0 0 2 1 0 2 2 2 2 2 1 1 0 2 0 1 0 1 0 2 0] Order of automorphism group: 486 The automorphism group has centre of order: 3 Number of regular subgroups: 4 Number of regular subgroups containing the center: 4 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 5> false [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 1 0 0 2 2 0 0 1 1 0 1 2 2 2 2 1 1 1 2 2 1 0 0 2] [0 0 1 1 2 2 2 0 1 1 1 0 2 0 0 0 1 2 0 2 1 0 2 2 1 2 1] [0 2 2 1 1 0 2 2 0 1 0 0 2 1 2 1 0 0 2 2 1 1 0 0 2 1 1] [0 0 0 2 0 2 2 1 1 1 2 1 1 1 0 2 0 1 2 1 0 1 2 0 2 2 0] [0 1 2 2 0 1 1 2 1 0 0 0 0 2 1 1 1 2 2 1 2 0 2 0 0 2 1] [0 2 1 1 0 1 0 0 2 1 0 2 1 0 1 2 0 0 1 0 2 2 2 1 2 2 1] [0 1 2 2 2 1 2 1 1 0 0 1 2 0 2 0 1 0 1 2 0 2 1 1 2 0 0] [0 1 2 0 1 0 2 1 2 1 1 0 1 2 0 1 0 2 1 0 0 2 1 2 0 2 2] [0 1 1 2 1 2 1 2 2 2 0 1 0 0 0 2 0 0 0 1 1 0 1 2 2 1 2] [0 2 0 2 1 0 1 1 0 1 1 1 2 2 1 0 2 2 0 0 2 0 2 1 2 1 0] [0 0 0 2 1 2 2 2 0 0 2 2 1 1 1 1 1 0 0 0 2 2 1 2 1 0 1] [0 1 0 1 1 0 0 0 2 0 2 1 2 0 2 0 2 1 2 1 2 1 1 2 0 2 1] [0 0 1 1 1 1 2 0 2 2 1 2 0 2 1 1 2 1 2 2 0 0 1 0 2 0 0] [0 2 1 0 2 0 1 1 1 2 2 0 1 1 0 2 2 0 2 2 2 0 1 1 0 0 1] [0 2 1 2 0 0 0 2 1 2 1 2 1 0 2 0 1 2 2 0 0 1 1 0 1 1 2] [0 2 1 2 2 2 0 2 2 0 1 0 2 2 0 1 0 1 1 1 2 1 0 1 1 0 0] [0 1 2 1 2 0 1 2 2 1 2 2 0 1 2 2 1 1 0 0 0 0 0 1 1 2 0] [0 2 2 0 1 2 1 0 1 2 2 1 0 2 2 0 0 1 1 0 1 2 2 0 1 0 1] [0 0 0 0 1 1 0 1 2 2 0 0 0 1 2 2 1 2 1 2 2 1 2 2 1 1 0] [0 0 0 2 2 1 1 2 2 1 2 0 1 0 1 0 2 1 1 2 1 2 0 0 0 1 2] [0 1 0 0 2 1 1 0 1 0 1 2 2 1 1 2 0 2 2 0 1 1 0 2 2 0 2] [0 2 1 0 0 1 0 1 0 0 2 1 1 2 2 1 1 1 0 2 1 0 0 2 2 2 2] [0 0 2 0 2 2 0 1 0 1 0 2 0 2 1 0 2 0 2 1 1 1 1 1 1 2 2] [0 1 2 0 0 1 2 1 0 2 1 2 2 0 0 2 2 1 0 1 2 2 0 0 1 1 1] [0 1 0 1 0 2 1 0 0 2 2 2 2 2 0 1 1 0 1 2 0 1 2 1 0 1 2] [0 2 2 1 2 2 0 0 1 2 0 1 1 1 1 1 2 2 0 1 0 2 0 2 0 1 0] Order of automorphism group: 486 The automorphism group has centre of order: 3 Number of regular subgroups: 4 Number of regular subgroups containing the center: 4 Expanded design is group developed over / Matrix is cocyclic over the following groups/ Extension splits: <81, 15> <27, 5> true <81, 7> <27, 3> false <81, 7> <27, 3> false <81, 13> <27, 5> false