degree:12
 order:45
[ 12, 6, 2, 24 ][ 4, 0, 3, 0, 2, 1 ]

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

 minimal polynomial of other basis elements:
 x^3-3*x^2-18*x
x^2-x-2
x^5-18*x^4-156*x^3+216*x^2+1728*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, 3, 2, 0, 6 ], [ 0, 4, 0, 0, 8 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 2, 1, 6 ] ], 
  [ [ 0, 0, 6, 0, 0 ], [ 0, 2, 0, 0, 4 ], [ 1, 0, 3, 2, 0 ], [ 0, 0, 6, 0, 0 ], [ 0, 2, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 1, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 4, 2, 12 ], [ 0, 8, 0, 0, 16 ], [ 0, 12, 0, 0, 12 ], [ 1, 6, 4, 1, 12 ] 
     ] ]


 Q-polynomial