degree:12
 order:45
[ 12, 6, 2, 6, 18 ][ 6, 12, 0, 4, 0, 6, 0, 0, 0, 2 ]

minimal polynomial:[ x-12, x, x^2-18, x^2+6*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-3*x^2-18*x
x^2-x-2
x^6-3*x^5-45*x^4+108*x^3+486*x^2-972*x
x^4-9*x^3-243*x^2+1458*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, 12, 0, 0, 0, 0 ], [ 1, 0, 3, 2, 0, 6 ], [ 0, 6, 0, 0, 6, 0 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 4, 0, 0, 2, 6 ] ], 
  [ [ 0, 0, 6, 0, 0, 0 ], [ 0, 3, 0, 0, 3, 0 ], [ 1, 0, 3, 2, 0, 0 ], 
      [ 0, 0, 6, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 0 ], [ 0, 0, 0, 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, 3, 0, 0, 3 ], [ 0, 6, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 2, 0, 3 ], [ 0, 2, 0, 0, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 0, 0, 0, 0, 0, 18 ], 
      [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 1, 6, 6, 2, 3, 0 ] ] ]