degree:8
 order:42
[ 8, 16, 1, 8, 8 ][ 2, 0, 1, 0, 0, 4, 4, 0, 1, 1 ]

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

 minimal polynomial of other basis elements:
 x^5-14*x^4-64*x^3+448*x^2+1024*x
x^2-1
x^5-8*x^4-20*x^3+144*x^2+128*x
x^5-2*x^4-46*x^3-44*x^2+208*x+128

 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, 2, 4, 0, 1, 0 ], [ 0, 2, 2, 0, 2, 2 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 1, 4, 0, 2, 1 ], [ 0, 0, 4, 1, 1, 2 ] ], 
  [ [ 0, 0, 16, 0, 0, 0 ], [ 0, 4, 4, 0, 4, 4 ], [ 1, 2, 6, 1, 4, 2 ], 
      [ 0, 0, 16, 0, 0, 0 ], [ 0, 4, 8, 0, 0, 4 ], [ 0, 4, 4, 0, 4, 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, 8, 0 ], [ 0, 1, 4, 0, 2, 1 ], [ 0, 2, 4, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 2, 0, 1, 2, 2 ], [ 0, 1, 4, 0, 2, 1 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 4, 1, 1, 2 ], [ 0, 2, 2, 0, 2, 2 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 1, 4, 0, 2, 1 ], [ 1, 2, 4, 0, 1, 0 ] ] ]