degree:8
 order:52
[ 8, 1, 18, 24 ][ 8, 0, 2, 0, 0, 6 ]

minimal polynomial:[ x-8, x, x+8, x^2-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^5-336*x^3+3888*x
x^3-22*x^2-48*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, 2, 0, 6, 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, 18, 0 ], [ 0, 0, 0, 0, 18 ], [ 0, 0, 0, 18, 0 ], [ 1, 0, 1, 0, 16 ], [ 0, 6, 0, 12, 0 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 0, 18, 0 ], [ 0, 0, 0, 0, 24 ], [ 0, 8, 0, 16, 0 ], [ 1, 0, 1, 0, 22 ] ] ]