degree:12
 order:30
[ 12, 9, 2, 6 ][ 8, 6, 2, 0, 6, 2 ]

minimal polynomial:[ x-12, x-3, x, x+2, x+8 ]   

 minimal polynomial of other basis elements:
[ x-9, x, x+3 ]
[ x-2, x+1 ]
[ x-6, x-2, x, x+3, 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, 3, 6, 1, 1 ], [ 0, 8, 0, 0, 4 ], [ 0, 6, 0, 0, 6 ], [ 0, 2, 6, 2, 2 ] ], 
  [ [ 0, 0, 9, 0, 0 ], [ 0, 6, 0, 0, 3 ], [ 1, 0, 6, 2, 0 ], [ 0, 0, 9, 0, 0 ], [ 0, 6, 0, 0, 3 ] ], 
  [ [ 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, 1, 3, 1, 1 ], [ 0, 4, 0, 0, 2 ], [ 0, 6, 0, 0, 0 ], [ 1, 2, 3, 0, 0 ] ] ]