degree:9
 order:40
[ 9, 9, 3, 18 ][ 1, 0, 3, 3, 2, 1 ]

minimal polynomial:[ x-9, x-3, x+1, x^2+4*x-1 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^5-9*x^4-14*x^3+110*x^2+141*x+27
x^2-2*x-3
x^5-16*x^4-56*x^3+320*x^2+720*x

 SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 9, 0, 0, 0 ], [ 1, 1, 1, 0, 6 ], [ 0, 1, 3, 1, 4 ], [ 0, 0, 3, 0, 6 ], [ 0, 3, 2, 1, 3 ] ], 
  [ [ 0, 0, 9, 0, 0 ], [ 0, 1, 3, 1, 4 ], [ 1, 3, 3, 0, 2 ], [ 0, 3, 0, 0, 6 ], [ 0, 2, 1, 1, 5 ] ], 
  [ [ 0, 0, 0, 3, 0 ], [ 0, 0, 1, 0, 2 ], [ 0, 1, 0, 0, 2 ], [ 1, 0, 0, 2, 0 ], [ 0, 1, 1, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 18 ], [ 0, 6, 4, 2, 6 ], [ 0, 4, 2, 2, 10 ], [ 0, 6, 6, 0, 6 ], [ 1, 3, 5, 1, 8 ] ] ]