degree:12
 order:60
[ 12, 12, 1, 2, 32 ][ 1, 0, 6, 3, 12, 6, 3, 0, 0, 0 ]

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

 minimal polynomial of other basis elements:
 x^6-8*x^5-72*x^4+240*x^3+720*x^2-1728*x
x^2-1
x^3-4*x
x^4-32*x^3-64*x^2+2048*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, 1, 1, 0, 1, 8 ], [ 0, 1, 1, 1, 1, 8 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 8 ], [ 1, 1, 1, 0, 1, 8 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 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, 2, 0 ], [ 0, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 2, 0 ], [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 32 ], [ 0, 8, 8, 0, 0, 16 ], [ 0, 8, 8, 0, 0, 16 ], 
      [ 0, 0, 0, 0, 0, 32 ], [ 0, 0, 0, 0, 0, 32 ], [ 1, 6, 6, 1, 2, 16 ] ] ]


 Q-polynomial