degree:10
 order:33
[ 10, 10, 2, 10 ][ 2, 0, 4, 5, 5, 1 ]

minimal polynomial:[ x-10, x+1, x+5, x^2-x-8 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^5-5*x^4-59*x^3+37*x^2+490*x+400
x^2-x-2
x^2-9*x-10

 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, 10, 0, 0, 0 ], [ 1, 3, 2, 0, 4 ], [ 0, 2, 2, 1, 5 ], [ 0, 0, 5, 0, 5 ], [ 0, 4, 5, 1, 0 ] ], 
  [ [ 0, 0, 10, 0, 0 ], [ 0, 2, 2, 1, 5 ], [ 1, 2, 3, 0, 4 ], [ 0, 5, 0, 0, 5 ], [ 0, 5, 4, 1, 0 ] ], 
  [ [ 0, 0, 0, 2, 0 ], [ 0, 0, 1, 0, 1 ], [ 0, 1, 0, 0, 1 ], [ 1, 0, 0, 1, 0 ], [ 0, 1, 1, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 10 ], [ 0, 4, 5, 1, 0 ], [ 0, 5, 4, 1, 0 ], [ 0, 5, 5, 0, 0 ], [ 1, 0, 0, 0, 9 ] ] ]