degree:4
 order:45
[ 4, 8, 16, 16 ][ 1, 0, 0, 1, 0, 2 ]

minimal polynomial:

[ x-4, x-3, x-1, x+1, x+2 ]
[ x-8, x-2, x+2, x+4 ]
[ x-16, x-6, x+2 ]
[ x-16, x-4, x-1, x+4 ]
SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ],
  [ [ 0, 4, 0, 0, 0 ], [ 1, 1, 2, 0, 0 ], [ 0, 1, 1, 2, 0 ], [ 0, 0, 1, 1, 2 ], [ 0, 0, 0, 2, 2 ] ],
  [ [ 0, 0, 8, 0, 0 ], [ 0, 2, 2, 4, 0 ], [ 1, 1, 0, 2, 4 ], [ 0, 1, 1, 2, 4 ], [ 0, 0, 2, 4, 2 ] ],
  [ [ 0, 0, 0, 16, 0 ], [ 0, 0, 4, 4, 8 ], [ 0, 2, 2, 4, 8 ], [ 1, 1, 2, 8, 4 ], [ 0, 2, 4, 4, 6 ] ],
  [ [ 0, 0, 0, 0, 16 ], [ 0, 0, 0, 8, 8 ], [ 0, 0, 4, 8, 4 ], [ 0, 2, 4, 4, 6 ], [ 1, 2, 2, 6, 5 ] ] ]