degree:12
 order:27
[ 12, 4, 4, 6 ][ 9, 6, 4, 0, 2, 4 ]

minimal polynomial:[ x-12, x-3, x, x+3, x+6 ] 
 Galois type:1

 minimal polynomial of other basis elements:
[ x-4, x-1, x+2 ]
[ x-4, x-1, x+2 ]
[ x-6, x-3, x, x+3 ]
 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, 4, 3, 2, 2 ], [ 0, 9, 0, 0, 3 ], [ 0, 6, 0, 0, 6 ], [ 0, 4, 2, 4, 2 ] ], 
  [ [ 0, 0, 4, 0, 0 ], [ 0, 3, 0, 0, 1 ], [ 1, 0, 1, 2, 0 ], [ 0, 0, 2, 2, 0 ], [ 0, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 4, 0 ], [ 0, 2, 0, 0, 2 ], [ 0, 0, 2, 2, 0 ], [ 1, 0, 2, 1, 0 ], [ 0, 4, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6 ], [ 0, 2, 1, 2, 1 ], [ 0, 3, 0, 0, 3 ], [ 0, 6, 0, 0, 0 ], [ 1, 2, 2, 0, 1 ] ] ]