degree:8
 order:56
[ 8, 32, 3, 4, 8 ][ 1, 8, 0, 0, 0, 0, 4, 0, 0, 4 ]

minimal polynomial:[ x-8, x-4, x, x+6, x^2-32 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-20*x^3-448*x^2+2048*x
x^2-2*x-3
x^3-16*x
x^6-6*x^5-72*x^4+384*x^3+1280*x^2-6144*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, 8, 0, 0, 0, 0 ], [ 1, 0, 4, 3, 0, 0 ], [ 0, 1, 6, 0, 0, 1 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 4, 0, 4, 0 ] ], 
  [ [ 0, 0, 32, 0, 0, 0 ], [ 0, 4, 24, 0, 0, 4 ], [ 1, 6, 12, 3, 4, 6 ], 
      [ 0, 0, 32, 0, 0, 0 ], [ 0, 0, 32, 0, 0, 0 ], [ 0, 4, 24, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 0 ], 
      [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 4 ], [ 0, 0, 4, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 3, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 4, 0, 4, 0 ], [ 0, 1, 6, 0, 0, 1 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 8, 0, 0, 0, 0 ], [ 1, 0, 4, 3, 0, 0 ] ] ]


 Q-polynomial