degree:12
 order:30
[ 12, 6, 3, 8 ][ 8, 4, 3, 0, 3, 3 ]

minimal polynomial:[ x-12, x-4, x, x+3, x+6 ]   

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