degree:12
 order:44
[ 12, 6, 4, 6, 6, 9 ][ 10, 0, 0, 6, 0, 2, 0, 0, 2, 4, 4, 4, 0 ]

minimal polynomial:[ x-12, x, x+12, x^4-34*x^2+44 ]
 Galois type:3

 minimal polynomial of other basis elements:
 x^4-8*x^3+3*x^2+52*x+12
x^7-32*x^5+300*x^3-704*x
x^7-50*x^5+548*x^3-1584*x
x^4-5*x^3-11*x^2+28*x+12
x^4-5*x^3-42*x^2+45*x+81

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ],
      [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0, 0, 0 ], [ 1, 0, 5, 0, 0, 3, 3 ], 
      [ 0, 10, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 9 ], 
      [ 0, 0, 2, 0, 0, 4, 6 ], [ 0, 6, 0, 2, 4, 0, 0 ], 
      [ 0, 4, 0, 4, 4, 0, 0 ] ], 
  [ [ 0, 0, 6, 0, 0, 0, 0 ], [ 0, 5, 0, 0, 1, 0, 0 ], [ 1, 0, 3, 0, 0, 2, 0 ],
      [ 0, 0, 0, 3, 3, 0, 0 ], [ 0, 2, 0, 2, 2, 0, 0 ], 
      [ 0, 0, 2, 0, 0, 1, 3 ], [ 0, 0, 0, 0, 0, 2, 4 ] ], 
  [ [ 0, 0, 0, 4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 3 ], [ 0, 0, 0, 2, 2, 0, 0 ],
      [ 1, 0, 3, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 2, 0 ], 
      [ 0, 2, 0, 0, 2, 0, 0 ], [ 0, 4, 0, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6, 0, 0 ], [ 0, 0, 1, 0, 0, 2, 3 ], [ 0, 2, 0, 2, 2, 0, 0 ],
      [ 0, 0, 3, 0, 0, 3, 0 ], [ 1, 0, 2, 0, 0, 0, 3 ], 
      [ 0, 4, 0, 2, 0, 0, 0 ], [ 0, 4, 0, 0, 2, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 6, 0 ], [ 0, 3, 0, 1, 2, 0, 0 ], [ 0, 0, 2, 0, 0, 1, 3 ],
      [ 0, 3, 0, 0, 3, 0, 0 ], [ 0, 4, 0, 2, 0, 0, 0 ], 
      [ 1, 0, 1, 0, 0, 1, 3 ], [ 0, 0, 2, 0, 0, 2, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 0, 9 ], [ 0, 3, 0, 3, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 6 ],
      [ 0, 9, 0, 0, 0, 0, 0 ], [ 0, 6, 0, 0, 3, 0, 0 ], 
      [ 0, 0, 3, 0, 0, 3, 3 ], [ 1, 0, 4, 0, 0, 2, 2 ] ] ]