degree:12
 order:54
[ 12, 12, 5, 12, 12 ][ 6, 12, 0, 0, 0, 0, 6, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x+6, x^3-108*x+216 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-6*x^5-180*x^4+864*x^3+6480*x^2-15552*x
x^2-4*x-5
x^6-6*x^5-180*x^4+864*x^3+6480*x^2-15552*x
x^3-6*x^2-72*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, 5, 0, 0 ], [ 0, 6, 0, 0, 0, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 6, 6 ], [ 0, 0, 6, 0, 6, 0 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 6 ], [ 1, 0, 0, 5, 6, 0 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 6, 0, 0, 6, 0 ] ], 
  [ [ 0, 0, 0, 5, 0, 0 ], [ 0, 5, 0, 0, 0, 0 ], [ 0, 0, 5, 0, 0, 0 ], 
      [ 1, 0, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 5, 0 ], [ 0, 0, 0, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 6, 6 ], [ 0, 0, 6, 0, 0, 6 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 6, 0, 5, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 6, 0, 6, 0 ], [ 0, 6, 0, 0, 6, 0 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 6, 0, 0, 0 ], [ 1, 0, 0, 5, 0, 6 ] ] ]