degree:12
 order:60
[ 12, 12, 2, 9, 24 ][ 1, 12, 0, 2, 0, 4, 4, 0, 0, 3 ]

minimal polynomial:[ x-12, x, x+3, x+4, x^2-2*x-39 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-9*x^2-36*x
x^2-x-2
x^3-6*x^2-27*x
x^6-14*x^5-284*x^4+360*x^3+14976*x^2+41472*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 4, 1, 2, 0, 4 ], [ 0, 1, 0, 0, 3, 8 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 8 ], [ 0, 2, 4, 0, 3, 3 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 0, 0, 3, 8 ], [ 1, 0, 9, 2, 0, 0 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 8 ], [ 0, 4, 0, 0, 3, 5 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], 
      [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 9, 0 ], [ 0, 0, 3, 0, 0, 6 ], [ 0, 3, 0, 0, 0, 6 ], 
      [ 0, 0, 0, 0, 9, 0 ], [ 1, 0, 0, 2, 6, 0 ], [ 0, 3, 3, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 4, 8, 0, 6, 6 ], [ 0, 8, 0, 0, 6, 10 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 8, 8, 0, 0, 8 ], [ 1, 3, 5, 2, 3, 10 ] ] ]