degree:8
 order:34
[ 8, 8, 1, 8, 8 ][ 4, 8, 2, 0, 0, 2, 2, 0, 0, 2 ]

minimal polynomial:[ x-8, x, x^4+2*x^3-24*x^2-8*x+16 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-6*x^5-40*x^4+184*x^3+80*x^2-128*x
x^2-1
x^6-6*x^5-40*x^4+184*x^3+80*x^2-128*x
x^6-6*x^5-40*x^4+184*x^3+80*x^2-128*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, 1, 2, 0 ], [ 0, 4, 0, 0, 2, 2 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 2, 2, 0, 2, 2 ], [ 0, 0, 2, 0, 2, 4 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 4, 0, 0, 2, 2 ], [ 1, 0, 0, 1, 4, 2 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 2, 4, 0, 0, 2 ], [ 0, 2, 2, 0, 2, 2 ] ], 
  [ [ 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, 8, 0 ], [ 0, 2, 2, 0, 2, 2 ], [ 0, 2, 4, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 2, 0, 1, 0, 4 ], [ 0, 2, 2, 0, 4, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 2, 0, 2, 4 ], [ 0, 2, 2, 0, 2, 2 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 2, 2, 0, 4, 0 ], [ 1, 4, 2, 1, 0, 0 ] ] ]