degree:6
 order:27
[ 6, 6, 2, 6, 6 ][ 1, 0, 2, 0, 3, 2, 2, 0, 1, 2 ]

minimal polynomial:[ x-6, x, x+3, x^3-9*x-9 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-3*x^5-27*x^4+18*x^3+189*x^2+162*x
x^2-x-2
x^3-3*x^2-18*x
x^6-3*x^5-27*x^4+18*x^3+189*x^2+162*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, 6, 0, 0, 0, 0 ], [ 1, 2, 1, 0, 2, 0 ], [ 0, 1, 0, 1, 2, 2 ], 
      [ 0, 0, 3, 0, 0, 3 ], [ 0, 2, 2, 0, 0, 2 ], [ 0, 0, 2, 1, 2, 1 ] ], 
  [ [ 0, 0, 6, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 2 ], [ 1, 0, 2, 0, 2, 1 ], 
      [ 0, 3, 0, 0, 0, 3 ], [ 0, 2, 2, 0, 0, 2 ], [ 0, 2, 1, 1, 2, 0 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 1, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 1 ], 
      [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 1, 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 2, 2, 0, 0, 2 ], [ 0, 2, 2, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 2, 3, 0 ], [ 0, 2, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 6 ], [ 0, 0, 2, 1, 2, 1 ], [ 0, 2, 1, 1, 2, 0 ], 
      [ 0, 3, 3, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 2 ], [ 1, 1, 0, 0, 2, 2 ] ] ]