degree:12
 order:50
[ 12, 12, 1, 12, 12 ][ 4, 12, 2, 0, 0, 4, 4, 0, 0, 4 ]

minimal polynomial:[ x-12, x, x^2-4*x-16, x^2+6*x+4 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-10*x^5-60*x^4+320*x^3+1280*x^2+768*x
x^2-1
x^6-10*x^5-60*x^4+320*x^3+1280*x^2+768*x
x^6-10*x^5-60*x^4+320*x^3+1280*x^2+768*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, 4, 4, 1, 2, 0 ], [ 0, 4, 0, 0, 4, 4 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 2, 4, 0, 2, 4 ], [ 0, 0, 4, 0, 4, 4 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 4, 4 ], [ 1, 0, 4, 1, 4, 2 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 4, 0, 0, 4 ], [ 0, 4, 2, 0, 4, 2 ] ], 
  [ [ 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, 12, 0 ], [ 0, 2, 4, 0, 2, 4 ], [ 0, 4, 4, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 2, 0, 1, 4, 4 ], [ 0, 4, 4, 0, 4, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 4, 0, 4, 4 ], [ 0, 4, 2, 0, 4, 2 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 4, 4, 0, 4, 0 ], [ 1, 4, 2, 1, 0, 4 ] ] ]