degree:12
 order:54
[ 12, 12, 2, 3, 24 ][ 3, 12, 0, 3, 0, 12, 3, 0, 0, 0 ]

minimal polynomial:[ x-12, x-3, x, x+6, x^2+3*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-12*x^5-63*x^4+702*x^3+1296*x^2-7776*x
x^2-x-2
x^3-9*x
x^4-18*x^3-216*x^2+1728*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 0, 3, 2, 0, 6 ], [ 0, 3, 0, 0, 3, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 12, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 3, 0, 0, 3, 6 ], [ 1, 0, 3, 2, 0, 6 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 12, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], 
      [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 3, 0, 0, 0 ], [ 0, 3, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 3, 0 ], [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 6, 6, 0, 0, 12 ], [ 0, 6, 6, 0, 0, 12 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 0, 0, 24 ], [ 1, 6, 6, 2, 3, 6 ] ] ]


 Q-polynomial