degree:12
 order:40
[ 12, 6, 1, 8, 12 ][ 2, 12, 3, 0, 0, 3, 3, 0, 0, 4 ]

minimal polynomial:[ x-12, x, x+3, x+4, x^2-7*x-14 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-4*x^2-12*x
x^2-1
x^3-6*x^2-16*x
x^6-2*x^5-111*x^4-240*x^3+1296*x^2+3456*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, 7, 1, 1, 2, 0 ], [ 0, 2, 0, 0, 4, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ], [ 0, 0, 3, 0, 4, 5 ] ], 
  [ [ 0, 0, 6, 0, 0, 0 ], [ 0, 1, 0, 0, 2, 3 ], [ 1, 0, 4, 1, 0, 0 ], 
      [ 0, 0, 6, 0, 0, 0 ], [ 0, 3, 0, 0, 0, 3 ], [ 0, 3, 0, 0, 2, 1 ] ], 
  [ [ 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, 8, 0 ], [ 0, 2, 2, 0, 0, 4 ], [ 0, 4, 0, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 0, 0, 1, 6, 0 ], [ 0, 4, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 3, 0, 4, 5 ], [ 0, 6, 0, 0, 4, 2 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 3, 0, 0, 3 ], [ 1, 5, 1, 1, 2, 2 ] ] ]