degree:12
 order:48
[ 12, 12, 3, 8, 12 ][ 2, 12, 0, 1, 0, 6, 6, 0, 0, 4 ]

minimal polynomial:[ x-12, x, x+4, x+6, x^2-4*x-44 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-8*x^2-48*x
x^2-2*x-3
x^3-4*x^2-32*x
x^6-6*x^5-132*x^4+184*x^3+5376*x^2+12672*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, 5, 2, 3, 0, 1 ], [ 0, 2, 0, 0, 4, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 1, 6, 0, 4, 1 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 2, 0, 0, 4, 6 ], [ 1, 0, 8, 3, 0, 0 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 6 ], [ 0, 6, 0, 0, 4, 2 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 0 ], 
      [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 8, 0 ], [ 0, 0, 4, 0, 0, 4 ], [ 0, 4, 0, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 0, 0, 3, 4, 0 ], [ 0, 4, 4, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 1, 6, 0, 4, 1 ], [ 0, 6, 0, 0, 4, 2 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 6, 0, 0, 0 ], [ 1, 1, 2, 3, 0, 5 ] ] ]