degree:9
 order:56
[ 9, 9, 1, 18, 18 ][ 1, 0, 2, 1, 9, 2, 1, 0, 0, 3 ]

minimal polynomial:[ x-9, x-3, x+3, x^3+x^2-9*x-1 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-8*x^5-27*x^4+152*x^3+171*x^2-720*x-81
x^2-1
x^5-16*x^4-72*x^3+640*x^2+144*x
x^5-16*x^4-72*x^3+640*x^2+144*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, 9, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 4, 2 ], [ 0, 1, 1, 1, 4, 2 ], 
      [ 0, 0, 9, 0, 0, 0 ], [ 0, 2, 2, 0, 2, 3 ], [ 0, 1, 1, 0, 3, 4 ] ], 
  [ [ 0, 0, 9, 0, 0, 0 ], [ 0, 1, 1, 1, 4, 2 ], [ 1, 1, 1, 0, 4, 2 ], 
      [ 0, 9, 0, 0, 0, 0 ], [ 0, 2, 2, 0, 2, 3 ], [ 0, 1, 1, 0, 3, 4 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 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, 18, 0 ], [ 0, 4, 4, 0, 4, 6 ], [ 0, 4, 4, 0, 4, 6 ], 
      [ 0, 0, 0, 0, 18, 0 ], [ 1, 2, 2, 1, 4, 8 ], [ 0, 3, 3, 0, 8, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 2, 2, 0, 6, 8 ], [ 0, 2, 2, 0, 6, 8 ], 
      [ 0, 0, 0, 0, 0, 18 ], [ 0, 3, 3, 0, 8, 4 ], [ 1, 4, 4, 1, 4, 4 ] ] ]