degree:12
 order:39
[ 12, 2, 12, 12 ][ 12, 3, 6, 0, 0, 3 ]

minimal polynomial:[ x-12, x, x^3+3*x^2-36*x+27 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-x-2
x^5-9*x^4-72*x^3+459*x^2-324*x
x^5-9*x^4-72*x^3+459*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, 0, 2, 3, 6 ], [ 0, 12, 0, 0, 0 ], [ 0, 3, 0, 6, 3 ], [ 0, 6, 0, 3, 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, 6, 3 ], [ 0, 0, 0, 12, 0 ], [ 1, 6, 2, 0, 3 ], [ 0, 3, 0, 3, 6 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 3, 3 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 0, 3, 6 ], [ 1, 3, 2, 6, 0 ] ] ]