degree:9
 order:42
[ 9, 2, 12, 18 ][ 9, 0, 3, 0, 0, 6 ]

minimal polynomial:[ x-9, x, x+9, x^2-18 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-x-2
x^5-162*x^3+2592*x
x^3-15*x^2-54*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, 0, 2, 0, 6 ], [ 0, 9, 0, 0, 0 ], [ 0, 0, 0, 0, 9 ], [ 0, 3, 0, 6, 0 ] ], 
  [ [ 0, 0, 2, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 1, 0, 1, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 2, 0, 9 ], [ 0, 6, 0, 6, 0 ] ], 
  [ [ 0, 0, 0, 0, 18 ], [ 0, 6, 0, 12, 0 ], [ 0, 0, 0, 0, 18 ], [ 0, 9, 0, 9, 0 ], [ 1, 0, 2, 0, 15 ] ] ]