degree:18
 order:32
[ 18, 1, 6, 6 ][ 18, 12, 9, 0, 0, 6 ]

minimal polynomial:[ x-18, x, x+6, x^2-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
[ x-1, x+1 ]
[ x-6, x, x+2 ]
[ x-6, x, x+2, x^2-12 ]

 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, 18, 0, 0, 0 ], [ 1, 9, 1, 4, 3 ], [ 0, 18, 0, 0, 0 ], [ 0, 12, 0, 0, 6 ], [ 0, 9, 0, 6, 3 ] ], 
  [ [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 6, 0 ], [ 0, 4, 0, 0, 2 ], [ 0, 0, 0, 6, 0 ], [ 1, 0, 1, 4, 0 ], [ 0, 6, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 6 ], [ 0, 3, 0, 2, 1 ], [ 0, 0, 0, 0, 6 ], [ 0, 6, 0, 0, 0 ], [ 1, 3, 1, 0, 1 ] ] ]