degree:12
 order:40
[ 12, 3, 4, 4, 4, 12 ][ 8, 0, 0, 6, 3, 0, 0, 0, 3, 2, 3, 3, 0 ]

minimal polynomial:[ x-12, x-3, x, x+3, x+12, x^2-5 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^7-22*x^5+101*x^3-80*x
x^3-16*x
x^2-3*x-4
x^4-6*x^3-67*x^2-72*x+144

 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, 2, 0, 0, 2, 7 ], 
      [ 0, 8, 0, 4, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 3, 6 ], 
      [ 0, 0, 0, 0, 0, 3, 9 ], [ 0, 6, 0, 3, 3, 0, 0 ], 
      [ 0, 7, 0, 2, 3, 0, 0 ] ], 
  [ [ 0, 0, 3, 0, 0, 0, 0 ], [ 0, 2, 0, 1, 0, 0, 0 ], [ 1, 0, 2, 0, 0, 0, 0 ],
      [ 0, 3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 1, 2 ] ], 
  [ [ 0, 0, 0, 4, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 2 ], [ 0, 4, 0, 0, 0, 0, 0 ],
      [ 1, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 1, 3 ], 
      [ 0, 3, 0, 0, 1, 0, 0 ], [ 0, 2, 0, 1, 1, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 3 ], [ 0, 0, 0, 0, 4, 0, 0 ],
      [ 0, 0, 0, 0, 0, 1, 3 ], [ 1, 0, 3, 0, 0, 0, 0 ], 
      [ 0, 3, 0, 1, 0, 0, 0 ], [ 0, 3, 0, 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 4, 0 ], [ 0, 2, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ],
      [ 0, 3, 0, 0, 1, 0, 0 ], [ 0, 3, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 3, 0 ], [ 0, 0, 1, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 0, 12 ], [ 0, 7, 0, 2, 3, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 4, 8 ], [ 0, 6, 0, 3, 3, 0, 0 ], 
      [ 0, 9, 0, 3, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 0, 9 ], 
      [ 1, 0, 2, 0, 0, 3, 6 ] ] ]