degree:6
 order:24
[ 6, 8, 3, 6 ][ 3, 2, 0, 0, 4, 2 ]

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

 minimal polynomial of other basis elements:
[ x-8, x, x+4 ]
[ x-3, x+1 ]
[ x-6, x-2, x, x+2, x+6 ]
 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, 4, 1, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 2, 0, 0, 4 ], [ 0, 0, 4, 2, 0 ] ], 
  [ [ 0, 0, 8, 0, 0 ], [ 0, 4, 0, 0, 4 ], [ 1, 0, 4, 3, 0 ], [ 0, 0, 8, 0, 0 ], [ 0, 4, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 3, 0 ], [ 0, 1, 0, 0, 2 ], [ 0, 0, 3, 0, 0 ], [ 1, 0, 0, 2, 0 ], [ 0, 2, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 6 ], [ 0, 0, 4, 2, 0 ], [ 0, 3, 0, 0, 3 ], [ 0, 4, 0, 0, 2 ], [ 1, 0, 4, 1, 0 ] ] ]