[0 0 0 0 0 0 0 0 0]
[0 1 2 0 1 2 0 1 2]
[0 2 1 0 2 1 0 2 1]
[0 0 0 1 1 1 2 2 2]
[0 1 2 1 2 0 2 0 1]
[0 2 1 1 0 2 2 1 0]
[0 0 0 2 2 2 1 1 1]
[0 1 2 2 0 1 1 2 0]
[0 2 1 2 1 0 1 0 2]

Order of automorphism group: 11664
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:
<27, 3> <9, 2> false
<27, 5> <9, 2> true
<27, 3> <9, 2> false
<27, 3> <9, 2> false
<27, 3> <9, 2> false
<27, 5> <9, 2> true
<27, 2> <9, 2> false
<27, 4> <9, 2> false



[0 0 0 0 0 0 0 0 0]
[0 2 2 2 1 1 1 0 0]
[0 2 1 1 0 2 2 1 0]
[0 2 1 0 2 1 0 2 1]
[0 1 0 2 0 2 1 2 1]
[0 1 2 1 2 0 2 0 1]
[0 1 2 0 1 2 0 1 2]
[0 0 1 2 2 0 1 1 2]
[0 0 0 1 1 1 2 2 2]

Order of automorphism group: 2916
The automorphism group has centre of order: 3
Number of regular subgroups: 1
Number of regular subgroups containing the center: 1
Expanded design is group developed over /
 Matrix is cocyclic over the following groups/ Extension splits:
<27, 2> <9, 1> true



[0 0 0 0 0 0 0 0 0]
[0 1 1 1 2 2 2 0 0]
[0 1 2 2 0 1 1 2 0]
[0 1 2 0 1 2 0 1 2]
[0 2 0 1 0 1 2 1 2]
[0 2 1 2 1 0 1 0 2]
[0 2 1 0 2 1 0 2 1]
[0 0 2 1 1 0 2 2 1]
[0 0 0 2 2 2 1 1 1]

Order of automorphism group: 2916
The automorphism group has centre of order: 3
Number of regular subgroups: 1
Number of regular subgroups containing the center: 1
Expanded design is group developed over /
 Matrix is cocyclic over the following groups/ Extension splits:
<27, 2> <9, 1> true