degree:12
 order:32
[ 12, 12, 3, 4 ][ 9, 8, 0, 0, 9, 3 ]

minimal polynomial:[ x-12, x-2, x, x+2, x+12 ] 
 Galois type:1

 minimal polynomial of other basis elements:
[ x-12, x, x+4 ]
[ x-3, x+1 ]
[ x-4, x-2, x, x+2, 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, 12, 0, 0, 0 ], [ 1, 0, 9, 2, 0 ], [ 0, 9, 0, 0, 3 ], [ 0, 8, 0, 0, 4 ], [ 0, 0, 9, 3, 0 ] ], 
  [ [ 0, 0, 12, 0, 0 ], [ 0, 9, 0, 0, 3 ], [ 1, 0, 8, 3, 0 ], [ 0, 0, 12, 0, 0 ], [ 0, 9, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 3, 0 ], [ 0, 2, 0, 0, 1 ], [ 0, 0, 3, 0, 0 ], [ 1, 0, 0, 2, 0 ], [ 0, 3, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 4 ], [ 0, 0, 3, 1, 0 ], [ 0, 3, 0, 0, 1 ], [ 0, 4, 0, 0, 0 ], [ 1, 0, 3, 0, 0 ] ] ]