degree:6
 order:40
[ 6, 6, 1, 2, 6, 18 ][ 1, 0, 3, 0, 1, 6, 3, 0, 1, 0, 0, 0, 0, 0, 2 ]

minimal polynomial:
[ x-6, x-3, x-2, x, x+2, x+3, x+4 ]
[ x-6, x-3, x, x+2, x+4 ]
[ x-1, x+1 ]
[ x-2, x, x+2 ]
[ x-6, x, x+4 ]
[ x-18, x-8, x, x+6 ]
 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, 1, 0, 3 ], [ 0, 1, 0, 1, 1, 0, 3 ], [ 0, 0, 6, 0, 0, 0, 0 ],
      [ 0, 3, 3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 6 ], [ 0, 1, 1, 0, 0, 2, 2 ] ],
  [ [ 0, 0, 6, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 3 ], [ 1, 0, 1, 0, 1, 0, 3 ], [ 0, 6, 0, 0, 0, 0, 0 ],
      [ 0, 3, 3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 6 ], [ 0, 1, 1, 0, 0, 2, 2 ] ],
  [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 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, 2, 0, 0 ], [ 0, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ],
      [ 1, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ],
  [ [ 0, 0, 0, 0, 0, 6, 0 ], [ 0, 0, 0, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 0, 6, 0 ],
      [ 0, 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 2, 2, 0 ], [ 0, 2, 2, 0, 0, 0, 2 ] ],
  [ [ 0, 0, 0, 0, 0, 0, 18 ], [ 0, 3, 3, 0, 0, 6, 6 ], [ 0, 3, 3, 0, 0, 6, 6 ], [ 0, 0, 0, 0, 0, 0, 18 ],
      [ 0, 0, 0, 0, 0, 0, 18 ], [ 0, 6, 6, 0, 0, 0, 6 ], [ 1, 2, 2, 1, 2, 2, 8 ] ] ]