degree:6
 order:24
[ 6, 1, 6, 10 ][ 6, 1, 0, 0, 0, 3 ]

minimal polynomial:[ x-6, x-5, x, x+2, x+3 ] 
 Galois type:1

 minimal polynomial of other basis elements:
[ x-1, x+1 ]
[ x-6, x, x+2 ]
[ x-10, x-2, x, x+5 ]
 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, 3, 1, 1, 0 ], [ 0, 6, 0, 0, 0 ], [ 0, 1, 0, 0, 5 ], [ 0, 0, 0, 3, 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, 1, 0, 0, 5 ], [ 0, 0, 0, 6, 0 ], [ 1, 0, 1, 4, 0 ], [ 0, 3, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 10 ], [ 0, 0, 0, 5, 5 ], [ 0, 0, 0, 0, 10 ], [ 0, 5, 0, 0, 5 ], [ 1, 3, 1, 3, 2 ] ] ]