degree:8
 order:32
[ 8, 14, 1, 8 ][ 4, 0, 0, 0, 7, 1 ]

minimal polynomial:[ x-8, x, x+8, x^2-8 ]
 Galois type:1

 minimal polynomial of other basis elements:
[ x-14, x, x+2 ]
[ x-1, x+1 ]
[ x-8, x, x+8, x^2-8 ]

 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, 8, 0, 0, 0 ], [ 1, 0, 7, 0, 0 ], [ 0, 4, 0, 0, 4 ], [ 0, 0, 0, 0, 8 ], [ 0, 0, 7, 1, 0 ] ], 
  [ [ 0, 0, 14, 0, 0 ], [ 0, 7, 0, 0, 7 ], [ 1, 0, 12, 1, 0 ], [ 0, 0, 14, 0, 0 ], [ 0, 7, 0, 0, 7 ] ], 
  [ [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 8 ], [ 0, 0, 7, 1, 0 ], [ 0, 4, 0, 0, 4 ], [ 0, 8, 0, 0, 0 ], [ 1, 0, 7, 0, 0 ] ] ]