degree:10
 order:30
[ 10, 2, 2, 5, 10 ][ 5, 0, 8, 4, 0, 0, 1, 2, 1, 0 ]

minimal polynomial:[ x-10, x+2, x^2-x-1, x^2+5*x-25 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-x^2-3*x+2
x^3-x^2-3*x+2
x^2-4*x-5
x^6-4*x^5-83*x^4+188*x^3+485*x^2-600*x-500

 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, 1, 0, 4, 4 ], [ 0, 5, 0, 0, 0, 5 ], 
      [ 0, 0, 0, 0, 5, 5 ], [ 0, 8, 0, 2, 0, 0 ], [ 0, 4, 1, 1, 0, 4 ] ], 
  [ [ 0, 0, 2, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1 ], [ 1, 0, 0, 1, 0, 0 ], 
      [ 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ], [ 0, 1, 0, 0, 1, 0 ] ], 
  [ [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 0, 0 ], 
      [ 1, 0, 1, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 5, 0 ], [ 0, 4, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 5 ], 
      [ 0, 5, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 4, 0 ], [ 0, 0, 1, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 10 ], [ 0, 4, 1, 1, 0, 4 ], [ 0, 5, 0, 0, 5, 0 ], 
      [ 0, 5, 0, 0, 0, 5 ], [ 0, 0, 2, 0, 0, 8 ], [ 1, 4, 0, 1, 4, 0 ] ] ]


 Q-polynomial