degree:6
 order:56
[ 6, 3, 6, 12, 12, 16 ][ 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 3 ]

minimal polynomial:
[ x-6, x, x+6, x^2-12, x^2-8 ]1
[ x-3, x+1 ]
[ x-6, x, x+6, x^2-12, x^2-8 ]
[ x-12, x-4, x+2 ]
[ x-12, x-2, x+2, x+4 ]
[ x-16, x, x+16, x^2-32 ]
 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, 6, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 4, 0, 0 ], [ 0, 2, 0, 4, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 4, 0 ],
      [ 0, 2, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 2, 0, 0, 4 ], [ 0, 0, 0, 0, 3, 3, 0 ] ],
  [ [ 0, 0, 3, 0, 0, 0, 0 ], [ 0, 1, 0, 2, 0, 0, 0 ], [ 1, 0, 2, 0, 0, 0, 0 ], [ 0, 2, 0, 1, 0, 0, 0 ],
      [ 0, 0, 0, 0, 1, 2, 0 ], [ 0, 0, 0, 0, 2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ],
  [ [ 0, 0, 0, 6, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 4, 0 ], [ 0, 4, 0, 2, 0, 0, 0 ], [ 1, 0, 1, 0, 4, 0, 0 ],
      [ 0, 0, 0, 2, 0, 0, 4 ], [ 0, 2, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 3, 3, 0 ] ],
  [ [ 0, 0, 0, 0, 12, 0, 0 ], [ 0, 4, 0, 0, 0, 0, 8 ], [ 0, 0, 0, 0, 4, 8, 0 ], [ 0, 0, 0, 4, 0, 0, 8 ],
      [ 1, 0, 1, 0, 6, 4, 0 ], [ 0, 0, 2, 0, 4, 6, 0 ], [ 0, 3, 0, 3, 0, 0, 6 ] ],
  [ [ 0, 0, 0, 0, 0, 12, 0 ], [ 0, 0, 0, 4, 0, 0, 8 ], [ 0, 0, 0, 0, 8, 4, 0 ], [ 0, 4, 0, 0, 0, 0, 8 ],
      [ 0, 0, 2, 0, 4, 6, 0 ], [ 1, 0, 1, 0, 6, 4, 0 ], [ 0, 3, 0, 3, 0, 0, 6 ] ],
  [ [ 0, 0, 0, 0, 0, 0, 16 ], [ 0, 0, 0, 0, 8, 8, 0 ], [ 0, 0, 0, 0, 0, 0, 16 ], [ 0, 0, 0, 0, 8, 8, 0 ],
      [ 0, 4, 0, 4, 0, 0, 8 ], [ 0, 4, 0, 4, 0, 0, 8 ], [ 1, 0, 3, 0, 6, 6, 0 ] ] ]