degree:12
 order:39
[ 12, 2, 12, 12 ][ 12, 3, 2, 0, 0, 7 ]

minimal polynomial:[ x-12, x, x^3+3*x^2-36*x-129 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-x-2
x^5-9*x^4-72*x^3+303*x^2+1548*x
x^5-9*x^4-72*x^3+303*x^2+1548*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, 3, 0, 2, 7 ], [ 0, 2, 0, 7, 3 ] ], 
  [ [ 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, 12, 0 ], [ 0, 3, 0, 2, 7 ], [ 0, 0, 0, 12, 0 ], 
      [ 1, 2, 2, 4, 3 ], [ 0, 7, 0, 3, 2 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 2, 0, 7, 3 ], [ 0, 0, 0, 0, 12 ], 
      [ 0, 7, 0, 3, 2 ], [ 1, 3, 2, 2, 4 ] ] ]