degree:6
 order:32
[ 6, 10, 5, 10 ][ 3, 0, 0, 0, 3, 3 ]

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

 minimal polynomial of other basis elements:
[ x-10, x-2, x+2 ]
[ x-5, x-1, x+3 ]
[ x-10, x, x+10, x^2-12 ]

 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, 6, 0, 0, 0 ], [ 1, 0, 5, 0, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 0, 0, 0, 6 ], [ 0, 0, 3, 3, 0 ] ], 
  [ [ 0, 0, 10, 0, 0 ], [ 0, 5, 0, 0, 5 ], [ 1, 0, 6, 3, 0 ], [ 0, 0, 6, 4, 0 ], [ 0, 3, 0, 0, 7 ] ], 
  [ [ 0, 0, 0, 5, 0 ], [ 0, 0, 0, 0, 5 ], [ 0, 0, 3, 2, 0 ], [ 1, 0, 4, 0, 0 ], [ 0, 3, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 10 ], [ 0, 0, 5, 5, 0 ], [ 0, 3, 0, 0, 7 ], [ 0, 6, 0, 0, 4 ], [ 1, 0, 7, 2, 0 ] ] ]