degree:12
 order:27
[ 12, 2, 6, 6 ][ 12, 6, 4, 0, 0, 6 ]

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

 minimal polynomial of other basis elements:
 x^2-x-2
x^3-3*x^2-18*x
x^5-3*x^4-36*x^3+54*x^2+324*x

 SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], 
      [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0 ], [ 1, 4, 2, 3, 2 ], [ 0, 12, 0, 0, 0 ], 
      [ 0, 6, 0, 0, 6 ], [ 0, 4, 0, 6, 2 ] ], 
  [ [ 0, 0, 2, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 1, 0, 1, 0, 0 ], 
      [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 6, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 0, 0, 6, 0 ], 
      [ 1, 0, 2, 3, 0 ], [ 0, 6, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6 ], [ 0, 2, 0, 3, 1 ], [ 0, 0, 0, 0, 6 ], 
      [ 0, 6, 0, 0, 0 ], [ 1, 2, 2, 0, 1 ] ] ]