degree:12
 order:27
[ 12, 6, 2, 6 ][ 8, 6, 4, 0, 4, 2 ]

minimal polynomial:[ x-12, x, x+6, x^2-6 ]
 Galois type:1

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