degree:10
 order:48
[ 10, 10, 3, 4, 20 ][ 1, 10, 0, 2, 0, 10, 2, 0, 0, 0 ]

minimal polynomial:[ x-10, x-4, x, x+6, x^2-40 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-8*x^5-84*x^4+560*x^3+1760*x^2-9600*x
x^2-2*x-3
x^3-16*x
x^4-8*x^3-304*x^2+1280*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, 1, 1, 3, 0, 4 ], [ 0, 1, 1, 0, 4, 4 ], 
      [ 0, 10, 0, 0, 0, 0 ], [ 0, 0, 10, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 6 ] ], 
  [ [ 0, 0, 10, 0, 0, 0 ], [ 0, 1, 1, 0, 4, 4 ], [ 1, 1, 1, 3, 0, 4 ], 
      [ 0, 0, 10, 0, 0, 0 ], [ 0, 10, 0, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 0 ], 
      [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 4, 0 ], [ 0, 0, 4, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 20 ], [ 0, 4, 4, 0, 0, 12 ], [ 0, 4, 4, 0, 0, 12 ], 
      [ 0, 0, 0, 0, 0, 20 ], [ 0, 0, 0, 0, 0, 20 ], [ 1, 6, 6, 3, 4, 0 ] ] ]


 Q-polynomial