degree:8
 order:48
[ 8, 3, 12, 24 ][ 8, 0, 1, 0, 0, 4 ]

minimal polynomial:[ x-8, x, x+4, x^2-32 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^3-8*x^2-48*x
x^5-12*x^4-320*x^3+384*x^2+9216*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, 1, 3, 0, 3 ], [ 0, 8, 0, 0, 0 ], [ 0, 0, 0, 0, 8 ], [ 0, 1, 0, 4, 3 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 3, 8, 0 ], [ 0, 4, 0, 0, 8 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 3, 0, 12, 9 ], [ 0, 0, 0, 0, 24 ], [ 0, 8, 0, 0, 16 ], [ 1, 3, 3, 8, 9 ] ] ]