degree:12
 order:56
[ 12, 12, 1, 6, 24 ][ 4, 12, 0, 3, 0, 4, 1, 0, 0, 2 ]

minimal polynomial:[ x-12, x-4, x, x+2, x^2+4*x-20 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-10*x^5-60*x^4+440*x^3+64*x^2-1920*x
x^2-1
x^3-4*x^2-12*x
x^5-16*x^4-208*x^3+256*x^2+3072*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, 0, 4, 1, 0, 6 ], [ 0, 4, 4, 0, 2, 2 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 8 ], [ 0, 3, 1, 0, 2, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 4, 0, 2, 2 ], [ 1, 4, 0, 1, 0, 6 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 8 ], [ 0, 1, 3, 0, 2, 6 ] ], 
  [ [ 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, 6, 0 ], [ 0, 0, 2, 0, 0, 4 ], [ 0, 2, 0, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 4, 0 ], [ 0, 2, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 6, 2, 0, 4, 12 ], [ 0, 2, 6, 0, 4, 12 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 8, 8, 0, 0, 8 ], [ 1, 6, 6, 1, 2, 8 ] ] ]