degree:12
 order:40
[ 12, 2, 1, 12, 12 ][ 6, 0, 4, 3, 0, 0, 1, 0, 1, 4 ]

minimal polynomial:[ x-12, x-2, x, x+4, x^2-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-4*x
x^2-1
x^4-8*x^3-80*x^2+384*x
x^6-10*x^5-44*x^4+216*x^3+384*x^2-1152*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, 3, 1, 0, 4, 3 ], [ 0, 6, 0, 0, 0, 6 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 4, 0, 0, 4, 4 ], [ 0, 3, 1, 1, 4, 3 ] ], 
  [ [ 0, 0, 2, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1 ], [ 1, 0, 0, 1, 0, 0 ], 
      [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 1, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 4, 0, 0, 4, 4 ], [ 0, 0, 0, 0, 12, 0 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 4, 2, 1, 0, 4 ], [ 0, 4, 0, 0, 4, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 1, 1, 4, 3 ], [ 0, 6, 0, 0, 0, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 4, 0, 0, 4, 4 ], [ 1, 3, 1, 0, 4, 3 ] ] ]


 Q-polynomial