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

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

 minimal polynomial of other basis elements:
 x^6-10*x^5-60*x^4+280*x^3+1664*x^2+1920*x
x^2-1
x^3-4*x^2-12*x
x^4-28*x^3+64*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, 5, 1, 1, 0, 4 ], [ 0, 1, 1, 0, 2, 8 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 8 ], [ 0, 2, 4, 0, 2, 4 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 1, 0, 2, 8 ], [ 1, 1, 5, 1, 0, 4 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 8 ], [ 0, 4, 2, 0, 2, 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, 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, 4, 8, 0, 4, 8 ], [ 0, 8, 4, 0, 4, 8 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 8, 8, 0, 0, 8 ], [ 1, 4, 4, 1, 2, 12 ] ] ]