degree:10
 order:42
[ 10, 10, 1, 10, 10 ][ 5, 0, 0, 4, 0, 5, 0, 0, 1, 5 ]

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

 minimal polynomial of other basis elements:
 x^3-9*x^2-15*x+50
x^2-1
x^6-111*x^4+1125*x^2-2500
x^3-9*x^2-15*x+50

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


 Q-polynomial