degree:12
 order:48
[ 12, 8, 3, 12, 12 ][ 3, 4, 4, 2, 0, 4, 2, 0, 2, 4 ]

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

 minimal polynomial of other basis elements:
 x^3-4*x^2-32*x
x^2-2*x-3
x^3-8*x^2-48*x
x^6-4*x^5-100*x^4-64*x^3+1312*x^2+768*x-4608

 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, 2, 2, 1, 4, 2 ], [ 0, 3, 0, 0, 6, 3 ], 
      [ 0, 4, 0, 0, 0, 8 ], [ 0, 4, 4, 0, 0, 4 ], [ 0, 2, 2, 2, 4, 2 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 2, 0, 0, 4, 2 ], [ 1, 0, 4, 3, 0, 0 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 4 ], [ 0, 2, 0, 0, 4, 2 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 1, 0, 0, 0, 2 ], [ 0, 0, 3, 0, 0, 0 ], 
      [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 2, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 4, 4, 0, 0, 4 ], [ 0, 6, 0, 0, 0, 6 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 0, 0, 3, 8, 0 ], [ 0, 4, 4, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 2, 2, 2, 4, 2 ], [ 0, 3, 0, 0, 6, 3 ], 
      [ 0, 8, 0, 0, 0, 4 ], [ 0, 4, 4, 0, 0, 4 ], [ 1, 2, 2, 1, 4, 2 ] ] ]