degree:12
 order:35
[ 12, 2, 2, 6, 12 ][ 6, 0, 4, 4, 0, 0, 1, 2, 1, 2 ]

minimal polynomial:[ x-12, x+2, x^4-18*x^2+36 ]
 Galois type:2

 minimal polynomial of other basis elements:
 x^3-x^2-3*x+2
x^3-x^2-3*x+2
x^4-5*x^3-12*x^2+30*x+36
x^6-10*x^5-42*x^4+180*x^3+468*x^2-360*x-864

 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, 4, 1, 0, 2, 4 ], [ 0, 6, 0, 0, 0, 6 ], 
      [ 0, 0, 0, 0, 6, 6 ], [ 0, 4, 0, 2, 2, 4 ], [ 0, 4, 1, 1, 2, 4 ] ], 
  [ [ 0, 0, 2, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1 ], [ 1, 0, 0, 1, 0, 0 ], 
      [ 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ], [ 0, 1, 0, 0, 1, 0 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 0, 0 ], 
      [ 1, 0, 1, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 2, 0, 1, 1, 2 ], [ 0, 0, 0, 0, 0, 6 ], 
      [ 0, 6, 0, 0, 0, 0 ], [ 1, 2, 0, 0, 1, 2 ], [ 0, 2, 1, 0, 1, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 4, 1, 1, 2, 4 ], [ 0, 6, 0, 0, 6, 0 ], 
      [ 0, 6, 0, 0, 0, 6 ], [ 0, 4, 2, 0, 2, 4 ], [ 1, 4, 0, 1, 2, 4 ] ] ]