degree:12
 order:56
[ 12, 3, 4, 12, 24 ][ 4, 0, 0, 5, 0, 2, 0, 0, 2, 5 ]

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

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^3-16*x
x^6-156*x^4+1760*x^2-4608
x^3-20*x^2-96*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, 0, 1, 0, 0, 10 ], [ 0, 4, 0, 0, 8, 0 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 2, 0, 0, 10 ], [ 0, 5, 0, 2, 5, 0 ] ], 
  [ [ 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, 0, 2, 0, 0, 10 ], [ 0, 8, 0, 0, 4, 0 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 1, 0, 1, 0, 0, 10 ], [ 0, 5, 0, 2, 5, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 10, 0, 4, 10, 0 ], [ 0, 0, 0, 0, 0, 24 ], 
      [ 0, 12, 0, 0, 12, 0 ], [ 0, 10, 0, 4, 10, 0 ], [ 1, 0, 3, 0, 0, 20 ] ] 
 ]


 Q-polynomial