degree:6
 order:42
[ 6, 18, 1, 4, 12 ][ 1, 6, 0, 0, 0, 0, 3, 0, 0, 2 ]

minimal polynomial:[ x-6, x-4, x, x+3, x^2+2*x-6 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-12*x^3-162*x^2+972*x
x^2-1
x^3-2*x^2-8*x
x^6-7*x^5-92*x^4+312*x^3+1152*x^2-3456*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, 1, 3, 1, 0, 0 ], [ 0, 1, 3, 0, 0, 2 ], 
      [ 0, 6, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 6 ], [ 0, 0, 3, 0, 2, 1 ] ], 
  [ [ 0, 0, 18, 0, 0, 0 ], [ 0, 3, 9, 0, 0, 6 ], [ 1, 3, 3, 1, 4, 6 ], 
      [ 0, 0, 18, 0, 0, 0 ], [ 0, 0, 18, 0, 0, 0 ], [ 0, 3, 9, 0, 0, 6 ] ], 
  [ [ 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, 0, 0, 0, 4 ], [ 0, 0, 4, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 1, 2, 0 ], [ 0, 2, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 6, 0, 4, 2 ], [ 0, 2, 6, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 0, 0, 0, 6 ], [ 1, 1, 6, 1, 2, 1 ] ] ]