degree:12
 order:56
[ 12, 3, 4, 12, 24 ][ 4, 0, 3, 2, 0, 2, 0, 0, 2, 2 ]

minimal polynomial:[ x-12, x-6, x+2, x+4, x^2-8 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^3-16*x
x^6-12*x^5-36*x^4+384*x^3+800*x^2-2304*x-4608
x^5-16*x^4-272*x^3+1536*x^2+9216*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, 3, 1, 0, 3, 4 ], [ 0, 4, 0, 0, 8, 0 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 2, 0, 3, 4 ], [ 0, 2, 0, 2, 2, 6 ] ], 
  [ [ 0, 0, 3, 0, 0, 0 ], [ 0, 1, 0, 0, 2, 0 ], [ 1, 0, 2, 0, 0, 0 ], 
      [ 0, 0, 0, 3, 0, 0 ], [ 0, 2, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 4, 0, 0 ], 
      [ 1, 0, 3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ], [ 0, 2, 0, 0, 2, 0 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 3, 2, 0, 3, 4 ], [ 0, 8, 0, 0, 4, 0 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 1, 3, 1, 0, 3, 4 ], [ 0, 2, 0, 2, 2, 6 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 4, 0, 4, 4, 12 ], [ 0, 0, 0, 0, 0, 24 ], 
      [ 0, 12, 0, 0, 12, 0 ], [ 0, 4, 0, 4, 4, 12 ], [ 1, 6, 3, 0, 6, 8 ] ] ]


 Q-polynomial