degree:6
 order:21
[ 6, 2, 6, 6 ][ 6, 3, 0, 0, 0, 3 ]

minimal polynomial:[ x-6, x, x^3+3*x^2-18*x-27 ]
 Galois type:1

 minimal polynomial of other basis elements:
[ x-2, x+1 ]
[ x-6, x, x^3+3*x^2-18*x-27 ]
[ x-6, x, x^3+3*x^2-18*x-27 ]
 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, 6, 0, 0, 0 ], [ 1, 0, 2, 3, 0 ], [ 0, 6, 0, 0, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 0, 0, 3, 3 ] ], 
  [ [ 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, 6, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 0, 0, 6, 0 ], [ 1, 0, 2, 0, 3 ], [ 0, 3, 0, 3, 0 ] ], 
  [ [ 0, 0, 0, 0, 6 ], [ 0, 0, 0, 3, 3 ], [ 0, 0, 0, 0, 6 ], [ 0, 3, 0, 3, 0 ], [ 1, 3, 2, 0, 0 ] ] ]