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

minimal polynomial:[ x-12, x-4, x, x+2, x+4 ] 
 Galois type:1

 minimal polynomial of other basis elements:
[ x-4, x, x+4 ]
[ x-3, x+1 ]
[ x-12, x-2, x, 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, 5, 2, 1, 3 ], [ 0, 6, 0, 0, 6 ], [ 0, 4, 0, 0, 8 ], [ 0, 3, 2, 2, 5 ] ], 
  [ [ 0, 0, 4, 0, 0 ], [ 0, 2, 0, 0, 2 ], [ 1, 0, 0, 3, 0 ], [ 0, 0, 4, 0, 0 ], [ 0, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 3, 0 ], [ 0, 1, 0, 0, 2 ], [ 0, 0, 3, 0, 0 ], [ 1, 0, 0, 2, 0 ], [ 0, 2, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 3, 2, 2, 5 ], [ 0, 6, 0, 0, 6 ], [ 0, 8, 0, 0, 4 ], [ 1, 5, 2, 1, 3 ] ] ]