degree:8
 order:30
[ 8, 8, 1, 4, 8 ][ 2, 8, 0, 1, 0, 4, 4, 0, 0, 2 ]

minimal polynomial:[ x-8, x, x+2, x+4, x^2-2*x-14 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-6*x^2-16*x
x^2-1
x^3-2*x^2-8*x
x^6-4*x^5-50*x^4+44*x^3+688*x^2+896*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, 3, 2, 1, 0, 1 ], [ 0, 2, 0, 0, 2, 4 ], 
      [ 0, 8, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 4 ], [ 0, 1, 4, 0, 2, 1 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 2, 0, 0, 2, 4 ], [ 1, 0, 6, 1, 0, 0 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 4 ], [ 0, 4, 0, 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, 4, 0 ], [ 0, 0, 2, 0, 0, 2 ], [ 0, 2, 0, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 1, 2, 0 ], [ 0, 2, 2, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 1, 4, 0, 2, 1 ], [ 0, 4, 0, 0, 2, 2 ], 
      [ 0, 0, 0, 0, 0, 8 ], [ 0, 4, 4, 0, 0, 0 ], [ 1, 1, 2, 1, 0, 3 ] ] ]