degree:12
 order:40
[ 12, 3, 12, 12 ][ 4, 3, 4, 2, 0, 4 ]

minimal polynomial:[ x-12, x-2, x+4, x^2-8 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^5-10*x^4-40*x^3+176*x^2+256*x-768
x^4-8*x^3-80*x^2+384*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, 1, 3, 4 ], [ 0, 4, 0, 8, 0 ], [ 0, 3, 2, 3, 4 ], [ 0, 4, 0, 4, 4 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 1, 0, 2, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 2, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 3, 2, 3, 4 ], [ 0, 8, 0, 4, 0 ], [ 1, 3, 1, 3, 4 ], [ 0, 4, 0, 4, 4 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 4, 0, 4, 4 ], [ 0, 0, 0, 0, 12 ], [ 0, 4, 0, 4, 4 ], [ 1, 4, 3, 4, 0 ] ] ]


 Q-polynomial