degree:12
 order:42
[ 12, 2, 3, 6, 6, 12 ][ 6, 0, 0, 6, 0, 2, 0, 0, 2, 2, 4, 3, 0 ]

minimal polynomial:[ x-12, x-2, x, x+2, x+12, x^2-7 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-x-2
x^3-9*x
x^7-44*x^5+295*x^3-252*x
x^2-5*x-6
x^4-5*x^3-80*x^2-60*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, 1, 0, 0, 3, 7 ], 
      [ 0, 6, 0, 0, 6, 0, 0 ], [ 0, 0, 0, 0, 0, 4, 8 ], 
      [ 0, 0, 2, 0, 0, 4, 6 ], [ 0, 6, 0, 2, 4, 0, 0 ], 
      [ 0, 7, 0, 2, 3, 0, 0 ] ], 
  [ [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 0, 0 ], [ 1, 0, 1, 0, 0, 0, 0 ],
      [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0, 1, 1 ] ], 
  [ [ 0, 0, 0, 3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 2 ], [ 0, 0, 0, 3, 0, 0, 0 ],
      [ 1, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 2 ], 
      [ 0, 2, 0, 0, 1, 0, 0 ], [ 0, 2, 0, 0, 1, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6, 0, 0 ], [ 0, 0, 1, 0, 0, 2, 3 ], [ 0, 6, 0, 0, 0, 0, 0 ],
      [ 0, 0, 0, 0, 0, 2, 4 ], [ 1, 0, 0, 0, 0, 1, 4 ], 
      [ 0, 4, 0, 1, 1, 0, 0 ], [ 0, 3, 0, 1, 2, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 6, 0 ], [ 0, 3, 0, 1, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 6 ],
      [ 0, 4, 0, 0, 2, 0, 0 ], [ 0, 4, 0, 1, 1, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 5, 0 ], [ 0, 0, 1, 0, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 0, 0, 0, 12 ], [ 0, 7, 0, 2, 3, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 6, 6 ], [ 0, 8, 0, 0, 4, 0, 0 ], 
      [ 0, 6, 0, 2, 4, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 10 ], 
      [ 1, 0, 1, 0, 0, 5, 5 ] ] ]