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

minimal polynomial:[ x-12, x-2, x, x+4, x^2-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-8*x^3-80*x^2+384*x
x^2-1
x^3-4*x
x^6-10*x^5-56*x^4+336*x^3+768*x^2-2304*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, 4, 1, 0, 3 ], [ 0, 4, 4, 0, 0, 4 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 4, 0, 2, 3 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 4, 0, 0, 4 ], [ 1, 4, 0, 1, 2, 4 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 4, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ], [ 0, 0, 2, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 2, 0 ], [ 1, 0, 0, 1, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 4, 0, 2, 3 ], [ 0, 4, 4, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 12, 0, 0, 0, 0 ], [ 1, 3, 4, 1, 0, 3 ] ] ]


 Q-polynomial