degree:4
 order:32
[ 4, 6, 9, 12 ][ 2, 0, 0, 0, 1, 3 ]

minimal polynomial:[ x-4, x, x+4, x^2-8 ]
 Galois type:1

 minimal polynomial of other basis elements:
[ x-6, x-2, x+2 ]
[ x-9, x-1, x+3 ]
[ x-12, x, x+12, x^2-8 ]

 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, 0, 3, 0, 0 ], [ 0, 2, 0, 0, 2 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 1, 3, 0 ] ], 
  [ [ 0, 0, 6, 0, 0 ], [ 0, 3, 0, 0, 3 ], [ 1, 0, 2, 3, 0 ], [ 0, 0, 2, 4, 0 ], [ 0, 1, 0, 0, 5 ] ], [ [ 0, 0, 0, 9, 0 ], [ 0, 0, 0, 0, 9 ], [ 0, 0, 3, 6, 0 ], [ 1, 0, 4, 4, 0 ], [ 0, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 0, 3, 9, 0 ], [ 0, 2, 0, 0, 10 ], [ 0, 4, 0, 0, 8 ], [ 1, 0, 5, 6, 0 ] ] ]