degree:12
 order:39
[ 12, 2, 12, 12 ][ 12, 2, 6, 0, 0, 4 ]

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

 minimal polynomial of other basis elements:
 x^2-x-2
x^5-9*x^4-72*x^3+420*x^2+144*x
x^5-9*x^4-72*x^3+420*x^2+144*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, 1, 2, 2, 6 ], [ 0, 12, 0, 0, 0 ], [ 0, 2, 0, 6, 4 ], [ 0, 6, 0, 4, 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, 12, 0 ], [ 0, 2, 0, 6, 4 ], [ 0, 0, 0, 12, 0 ], [ 1, 6, 2, 1, 2 ], [ 0, 4, 0, 2, 6 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 4, 2 ], [ 0, 0, 0, 0, 12 ], [ 0, 4, 0, 2, 6 ], [ 1, 2, 2, 6, 1 ] ] ]