degree:12
 order:60
[ 12, 2, 18, 27 ][ 12, 0, 4, 0, 0, 8 ]

minimal polynomial:[ x-12, x, x+12, x^2-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-x-2
x^5-348*x^3+7776*x
x^3-24*x^2-81*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, 0, 9 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 4, 0, 8, 0 ] ], 
  [ [ 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, 18, 0 ], [ 0, 0, 0, 0, 18 ], [ 0, 0, 0, 18, 0 ], [ 1, 0, 2, 0, 15 ], [ 0, 8, 0, 10, 0 ] ],
  [ [ 0, 0, 0, 0, 27 ], [ 0, 9, 0, 18, 0 ], [ 0, 0, 0, 0, 27 ], [ 0, 12, 0, 15, 0 ], [ 1, 0, 2, 0, 24 ] 
     ] ]