degree:12
 order:51
[ 12, 12, 2, 12, 12 ][ 6, 12, 3, 0, 0, 3, 3, 0, 0, 3 ]

minimal polynomial:[ x-12, x, x^4+3*x^3-54*x^2-27*x+81 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-9*x^5-90*x^4+621*x^3+405*x^2-972*x
x^2-x-2
x^6-9*x^5-90*x^4+621*x^3+405*x^2-972*x
x^6-9*x^5-90*x^4+621*x^3+405*x^2-972*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, 6, 2, 3, 0 ], [ 0, 6, 0, 0, 3, 3 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 3, 3 ], [ 0, 0, 3, 0, 3, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 0, 0, 3, 3 ], [ 1, 0, 0, 2, 6, 3 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 3, 6, 0, 0, 3 ], [ 0, 3, 3, 0, 3, 3 ] ], 
  [ [ 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, 12, 0 ], [ 0, 3, 3, 0, 3, 3 ], [ 0, 3, 6, 0, 0, 3 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 3, 0, 2, 0, 6 ], [ 0, 3, 3, 0, 6, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 3, 0, 3, 6 ], [ 0, 3, 3, 0, 3, 3 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 3, 0, 6, 0 ], [ 1, 6, 3, 2, 0, 0 ] ] ]