degree:12
 order:36
[ 12, 10, 1, 12 ][ 6, 0, 3, 0, 5, 1 ]

minimal polynomial:[ x-12, x, x+6, x^2-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-8*x^2-20*x
x^2-1
x^5-6*x^4-84*x^3+72*x^2+864*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, 5, 0, 3 ], [ 0, 6, 0, 0, 6 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 5, 1, 3 ] ], 
  [ [ 0, 0, 10, 0, 0 ], [ 0, 5, 0, 0, 5 ], [ 1, 0, 8, 1, 0 ], [ 0, 0, 10, 0, 0 ], [ 0, 5, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 3, 5, 1, 3 ], [ 0, 6, 0, 0, 6 ], [ 0, 12, 0, 0, 0 ], [ 1, 3, 5, 0, 3 ] ] ]


 Q-polynomial