degree:12
 order:45
[ 12, 6, 2, 6, 6, 12 ][ 6, 12, 6, 0, 0, 0, 6, 0, 0, 0, 0, 3, 3 ]

minimal polynomial:[ x-12, x, x+6, x^2-3*x-9, x^2+6*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-3*x^2-18*x
x^2-x-2
x^4-3*x^3-27*x^2+54*x
x^4-3*x^3-27*x^2+54*x
x^7-3*x^6-153*x^5+216*x^4+4536*x^3-5832*x^2-23328*x

 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, 3, 2, 3, 0, 3 ], 
      [ 0, 6, 0, 0, 0, 6, 0 ], [ 0, 12, 0, 0, 0, 0, 0 ], 
      [ 0, 6, 0, 0, 0, 0, 6 ], [ 0, 0, 6, 0, 0, 0, 6 ], 
      [ 0, 3, 0, 0, 3, 3, 3 ] ], 
  [ [ 0, 0, 6, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0, 3, 0 ], [ 1, 0, 3, 2, 0, 0, 0 ],
      [ 0, 0, 6, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 6 ], 
      [ 0, 6, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3, 0, 3 ] ], 
  [ [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ],
      [ 1, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], 
      [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 6, 0, 0 ], [ 0, 3, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 6 ],
      [ 0, 0, 0, 0, 6, 0, 0 ], [ 1, 0, 0, 2, 0, 3, 0 ], 
      [ 0, 0, 0, 0, 3, 3, 0 ], [ 0, 3, 3, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 6, 0 ], [ 0, 0, 3, 0, 0, 0, 3 ], [ 0, 6, 0, 0, 0, 0, 0 ],
      [ 0, 0, 0, 0, 0, 6, 0 ], [ 0, 0, 0, 0, 3, 3, 0 ], 
      [ 1, 0, 0, 2, 3, 0, 0 ], [ 0, 3, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 0, 12 ], [ 0, 3, 0, 0, 3, 3, 3 ], 
      [ 0, 0, 0, 0, 6, 0, 6 ], [ 0, 0, 0, 0, 0, 0, 12 ], 
      [ 0, 6, 6, 0, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 0, 6 ], 
      [ 1, 3, 3, 2, 0, 3, 0 ] ] ]