degree:8
 order:40
[ 8, 16, 1, 6, 8 ][ 2, 0, 4, 0, 0, 0, 4, 0, 1, 3 ]

minimal polynomial:[ x-8, x, x^2-8, x^2+4*x-16 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-8*x^3-192*x^2+1024*x
x^2-1
x^3-4*x^2-12*x
x^6-4*x^5-56*x^4+160*x^3+384*x^2-1024*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, 0, 3, 0 ], [ 0, 2, 4, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 4, 0, 0, 0, 4 ], [ 0, 0, 4, 1, 3, 0 ] ], 
  [ [ 0, 0, 16, 0, 0, 0 ], [ 0, 4, 8, 0, 0, 4 ], [ 1, 4, 0, 1, 6, 4 ], 
      [ 0, 0, 16, 0, 0, 0 ], [ 0, 0, 16, 0, 0, 0 ], [ 0, 4, 8, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 3, 0, 0, 0, 3 ], [ 0, 0, 6, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 4, 0 ], [ 0, 3, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 4, 1, 3, 0 ], [ 0, 2, 4, 0, 0, 2 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 4 ], [ 1, 0, 4, 0, 3, 0 ] ] ]