degree:8
 order:28
[ 8, 1, 6, 12 ][ 8, 0, 4, 0, 0, 4 ]

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

 minimal polynomial of other basis elements:
 x^2-1
x^5-44*x^3+288*x
x^3-10*x^2-24*x

 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, 1, 0, 6 ], [ 0, 8, 0, 0, 0 ], [ 0, 0, 0, 0, 8 ], [ 0, 4, 0, 4, 0 ] ], 
  [ [ 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, 0, 0, 0, 6 ], [ 0, 0, 0, 6, 0 ], [ 1, 0, 1, 0, 4 ], [ 0, 4, 0, 2, 0 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 6, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 8, 0, 4, 0 ], [ 1, 0, 1, 0, 10 ] ] ]