degree:4
 order:25
[ 4, 4, 4, 4, 8 ][ 2, 1, 0, 0, 0, 0, 1, 0, 1, 1 ]

minimal polynomial:[ x-4, x+1, x^2-3*x+1, x^2+2*x-4 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-4*x^5-10*x^4+45*x^3-10*x^2-44*x+16
x^6-4*x^5-10*x^4+45*x^3-10*x^2-44*x+16
x^6-4*x^5-10*x^4+45*x^3-10*x^2-44*x+16
x^3-9*x^2+2*x+48

 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, 4, 0, 0, 0, 0 ], [ 1, 0, 2, 1, 0, 0 ], [ 0, 2, 0, 0, 0, 2 ], 
      [ 0, 1, 0, 1, 0, 2 ], [ 0, 0, 0, 0, 2, 2 ], [ 0, 0, 1, 1, 1, 1 ] ], 
  [ [ 0, 0, 4, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 2 ], [ 1, 0, 0, 2, 1, 0 ], 
      [ 0, 0, 2, 0, 0, 2 ], [ 0, 0, 1, 0, 1, 2 ], [ 0, 1, 0, 1, 1, 1 ] ], 
  [ [ 0, 0, 0, 4, 0, 0 ], [ 0, 1, 0, 1, 0, 2 ], [ 0, 0, 2, 0, 0, 2 ], 
      [ 1, 1, 0, 0, 2, 0 ], [ 0, 0, 0, 2, 0, 2 ], [ 0, 1, 1, 0, 1, 1 ] ], 
  [ [ 0, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 2, 2 ], [ 0, 0, 1, 0, 1, 2 ], 
      [ 0, 0, 0, 2, 0, 2 ], [ 1, 2, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 2, 2, 2, 2 ], [ 0, 2, 0, 2, 2, 2 ], 
      [ 0, 2, 2, 0, 2, 2 ], [ 0, 2, 2, 2, 0, 2 ], [ 1, 1, 1, 1, 1, 3 ] ] ]