degree:5
 order:24
[ 5, 10, 1, 2, 5 ][ 2, 0, 0, 0, 0, 5, 4, 0, 1, 0 ]

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

 minimal polynomial of other basis elements:
 x^3-8*x^2-20*x
x^2-1
x^3-4*x
x^6-31*x^4+155*x^2-125

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


 Q-polynomial