degree:8
 order:45
[ 8, 8, 4, 24 ][ 1, 0, 2, 2, 1, 1 ]

minimal polynomial:[ x-8, x+1, x^3-12*x+14 ]
 Galois type:2

 minimal polynomial of other basis elements:
 x^5-7*x^4-20*x^3+88*x^2+68*x-32
x^2-3*x-4
x^5-21*x^4-90*x^3+396*x^2+918*x-1296

 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, 1, 3, 1, 3 ], [ 0, 0, 2, 0, 6 ], [ 0, 2, 1, 1, 4 ] ], 
  [ [ 0, 0, 8, 0, 0 ], [ 0, 1, 3, 1, 3 ], [ 1, 3, 1, 0, 3 ], [ 0, 2, 0, 0, 6 ], [ 0, 1, 1, 1, 5 ] ], 
  [ [ 0, 0, 0, 4, 0 ], [ 0, 0, 1, 0, 3 ], [ 0, 1, 0, 0, 3 ], [ 1, 0, 0, 3, 0 ], [ 0, 1, 1, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 3, 3, 12 ], [ 0, 3, 3, 3, 15 ], [ 0, 6, 6, 0, 12 ], [ 1, 4, 5, 2, 12 ] ] ]