degree:12
 order:42
[ 12, 4, 1, 6, 18 ][ 6, 12, 2, 4, 0, 4, 0, 0, 0, 2 ]

minimal polynomial:[ x-12, x-3, x, x+4, x^2+4*x-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-2*x^2-8*x
x^2-1
x^6-5*x^5-26*x^4+102*x^3+180*x^2-432*x
x^4-12*x^3-162*x^2+972*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, 1, 2, 1, 1, 6 ], [ 0, 6, 0, 0, 6, 0 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 2, 4, 0, 0, 6 ], [ 0, 4, 0, 0, 2, 6 ] ], 
  [ [ 0, 0, 4, 0, 0, 0 ], [ 0, 2, 0, 0, 2, 0 ], [ 1, 0, 2, 1, 0, 0 ], 
      [ 0, 0, 4, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 1, 2, 0, 0, 3 ], [ 0, 6, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 1, 3 ], [ 0, 2, 0, 0, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 0, 0, 0, 0, 0, 18 ], 
      [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 0, 0, 3, 9 ], [ 1, 6, 4, 1, 3, 3 ] ] ]