degree:10
 order:45
[ 10, 10, 4, 10, 10 ][ 5, 10, 0, 0, 0, 0, 5, 0, 0, 5 ]

minimal polynomial:[ x-10, x, x+5, x^3-75*x+125 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-5*x^5-125*x^4+500*x^3+3125*x^2-6250*x
x^2-3*x-4
x^6-5*x^5-125*x^4+500*x^3+3125*x^2-6250*x
x^3-5*x^2-50*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 10, 0, 0, 0, 0 ], [ 1, 0, 5, 4, 0, 0 ], [ 0, 5, 0, 0, 0, 5 ], 
      [ 0, 10, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5, 5 ], [ 0, 0, 5, 0, 5, 0 ] ], 
  [ [ 0, 0, 10, 0, 0, 0 ], [ 0, 5, 0, 0, 0, 5 ], [ 1, 0, 0, 4, 5, 0 ], 
      [ 0, 0, 10, 0, 0, 0 ], [ 0, 0, 5, 0, 0, 5 ], [ 0, 5, 0, 0, 5, 0 ] ], 
  [ [ 0, 0, 0, 4, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 0 ], 
      [ 1, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 10, 0 ], [ 0, 0, 0, 0, 5, 5 ], [ 0, 0, 5, 0, 0, 5 ], 
      [ 0, 0, 0, 0, 10, 0 ], [ 1, 5, 0, 4, 0, 0 ], [ 0, 5, 5, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 10 ], [ 0, 0, 5, 0, 5, 0 ], [ 0, 5, 0, 0, 5, 0 ], 
      [ 0, 0, 0, 0, 0, 10 ], [ 0, 5, 5, 0, 0, 0 ], [ 1, 0, 0, 4, 0, 5 ] ] ]