degree:12
 order:44
[ 12, 1, 10, 20 ][ 12, 6, 3, 0, 0, 3 ]

minimal polynomial:[ x-12, x-3, x, x^2+9*x+12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^4-8*x^3-52*x^2+320*x
x^5-22*x^4+9*x^3+640*x^2-400*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, 0, 1, 5, 5 ], [ 0, 12, 0, 0, 0 ], 
      [ 0, 6, 0, 0, 6 ], [ 0, 3, 0, 3, 6 ] ], 
  [ [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 10, 0 ], [ 0, 5, 0, 0, 5 ], [ 0, 0, 0, 10, 0 ], 
      [ 1, 0, 1, 0, 8 ], [ 0, 3, 0, 4, 3 ] ], 
  [ [ 0, 0, 0, 0, 20 ], [ 0, 5, 0, 5, 10 ], [ 0, 0, 0, 0, 20 ], 
      [ 0, 6, 0, 8, 6 ], [ 1, 6, 1, 3, 9 ] ] ]