degree:6
 order:45
[ 6, 18, 2, 6, 12 ][ 1, 6, 0, 0, 0, 0, 3, 0, 0, 3 ]

minimal polynomial:[ x-6, x, x^2-18, x^2+3*x-9 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-9*x^3-243*x^2+1458*x
x^2-x-2
x^3-3*x^2-18*x
x^6-6*x^5-126*x^4+540*x^3+1944*x^2-7776*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, 0, 3, 2, 0, 0 ], [ 0, 1, 3, 0, 0, 2 ], 
      [ 0, 6, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 6 ], [ 0, 0, 3, 0, 3, 0 ] ], 
  [ [ 0, 0, 18, 0, 0, 0 ], [ 0, 3, 9, 0, 0, 6 ], [ 1, 3, 0, 2, 6, 6 ], 
      [ 0, 0, 18, 0, 0, 0 ], [ 0, 0, 18, 0, 0, 0 ], [ 0, 3, 9, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], 
      [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 0, 0, 0, 0, 6 ], [ 0, 0, 6, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 2, 3, 0 ], [ 0, 3, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 6, 0, 6, 0 ], [ 0, 2, 6, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 0, 0, 0, 6 ], [ 1, 0, 6, 2, 3, 0 ] ] ]