degree:5
 order:32
[ 5, 20, 1, 5 ][ 1, 0, 0, 0, 4, 1 ]

minimal polynomial:[ x-5, x-1, x+3, x^2-5 ]
 Galois type:1

 minimal polynomial of other basis elements:
[ x-20, x-4, x, x+4 ]
[ x-1, x+1 ]
[ x-5, x-1, x+3, x^2-5 ]

 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, 5, 0, 0, 0 ], [ 1, 0, 4, 0, 0 ], [ 0, 1, 3, 0, 1 ], [ 0, 0, 0, 0, 5 ], [ 0, 0, 4, 1, 0 ] ], 
  [ [ 0, 0, 20, 0, 0 ], [ 0, 4, 12, 0, 4 ], [ 1, 3, 12, 1, 3 ], [ 0, 0, 20, 0, 0 ], [ 0, 4, 12, 0, 4 ] ], 
  [ [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 5 ], [ 0, 0, 4, 1, 0 ], [ 0, 1, 3, 0, 1 ], [ 0, 5, 0, 0, 0 ], [ 1, 0, 4, 0, 0 ] ] ]