degree:12
 order:45
[ 12, 4, 4, 6, 18 ][ 9, 6, 0, 4, 0, 2, 0, 4, 0, 2 ]

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

 minimal polynomial of other basis elements:
 x^3-3*x^2-6*x+8
x^3-3*x^2-6*x+8
x^6-3*x^5-36*x^4+81*x^3+243*x^2-486*x
x^4-9*x^3-243*x^2+1458*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, 9, 0, 0, 3, 0 ], 
      [ 0, 6, 0, 0, 6, 0 ], [ 0, 0, 2, 4, 0, 6 ], [ 0, 4, 0, 0, 2, 6 ] ], 
  [ [ 0, 0, 4, 0, 0, 0 ], [ 0, 3, 0, 0, 1, 0 ], [ 1, 0, 1, 2, 0, 0 ], 
      [ 0, 0, 2, 2, 0, 0 ], [ 0, 2, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 4, 0, 0 ], [ 0, 2, 0, 0, 2, 0 ], [ 0, 0, 2, 2, 0, 0 ], 
      [ 1, 0, 2, 1, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 0, 1, 2, 0, 3 ], [ 0, 3, 0, 0, 3, 0 ], 
      [ 0, 6, 0, 0, 0, 0 ], [ 1, 0, 2, 0, 0, 3 ], [ 0, 2, 0, 0, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 0, 0, 0, 0, 0, 18 ], 
      [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 1, 6, 4, 4, 3, 0 ] ] ]