degree:8
 order:36
[ 8, 8, 3, 8, 8 ][ 4, 8, 0, 0, 0, 0, 4, 0, 0, 4 ]

minimal polynomial:[ x-8, x, x+4, x^3-48*x+64 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-4*x^5-80*x^4+256*x^3+1280*x^2-2048*x
x^2-2*x-3
x^6-4*x^5-80*x^4+256*x^3+1280*x^2-2048*x
x^3-4*x^2-32*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, 4, 0, 0, 0, 4 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4, 4 ], [ 0, 0, 4, 0, 4, 0 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 4 ], [ 1, 0, 0, 3, 4, 0 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 4 ], [ 0, 4, 0, 0, 4, 0 ] ], 
  [ [ 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, 8, 0 ], [ 0, 0, 0, 0, 4, 4 ], [ 0, 0, 4, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 4, 0, 3, 0, 0 ], [ 0, 4, 4, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 4, 0, 4, 0 ], [ 0, 4, 0, 0, 4, 0 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 4, 4, 0, 0, 0 ], [ 1, 0, 0, 3, 0, 4 ] ] ]