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

minimal polynomial:[ x-8, x, x^2-8, x^2+2*x-20 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-6*x^5-44*x^4+208*x^3+288*x^2-1280*x
x^2-1
x^5-8*x^4-20*x^3+144*x^2+128*x
x^5-12*x^4-88*x^3+352*x^2+512*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, 2, 1, 0, 4 ], [ 0, 2, 2, 0, 4, 0 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 4 ], [ 0, 2, 0, 0, 2, 4 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 2, 2, 0, 4, 0 ], [ 1, 2, 0, 1, 0, 4 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 4 ], [ 0, 0, 2, 0, 2, 4 ] ], 
  [ [ 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, 0, 4, 0, 0, 4 ], [ 0, 4, 0, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 0, 0, 1, 2, 4 ], [ 0, 2, 2, 0, 2, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 16 ], [ 0, 4, 0, 0, 4, 8 ], [ 0, 0, 4, 0, 4, 8 ], 
      [ 0, 0, 0, 0, 0, 16 ], [ 0, 4, 4, 0, 4, 4 ], [ 1, 4, 4, 1, 2, 4 ] ] ]