degree:8
 order:41
[ 8, 8, 8, 8, 8 ][ 3, 2, 2, 0, 1, 2, 2, 1, 2, 1 ]

minimal polynomial:[ x-8, x^5+x^4-16*x^3+5*x^2+21*x-9 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-7*x^5-24*x^4+133*x^3-19*x^2-177*x+72
x^6-7*x^5-24*x^4+133*x^3-19*x^2-177*x+72
x^6-7*x^5-24*x^4+133*x^3-19*x^2-177*x+72
x^6-7*x^5-24*x^4+133*x^3-19*x^2-177*x+72

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 8, 0, 0, 0, 0 ], [ 1, 0, 3, 2, 2, 0 ], [ 0, 3, 0, 1, 2, 2 ], 
      [ 0, 2, 1, 2, 1, 2 ], [ 0, 2, 2, 1, 2, 1 ], [ 0, 0, 2, 2, 1, 3 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 3, 0, 1, 2, 2 ], [ 1, 0, 0, 2, 3, 2 ], 
      [ 0, 1, 2, 2, 2, 1 ], [ 0, 2, 3, 2, 0, 1 ], [ 0, 2, 2, 1, 1, 2 ] ], 
  [ [ 0, 0, 0, 8, 0, 0 ], [ 0, 2, 1, 2, 1, 2 ], [ 0, 1, 2, 2, 2, 1 ], 
      [ 1, 2, 2, 0, 0, 3 ], [ 0, 1, 2, 0, 3, 2 ], [ 0, 2, 1, 3, 2, 0 ] ], 
  [ [ 0, 0, 0, 0, 8, 0 ], [ 0, 2, 2, 1, 2, 1 ], [ 0, 2, 3, 2, 0, 1 ], 
      [ 0, 1, 2, 0, 3, 2 ], [ 1, 2, 0, 3, 0, 2 ], [ 0, 1, 1, 2, 2, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 8 ], [ 0, 0, 2, 2, 1, 3 ], [ 0, 2, 2, 1, 1, 2 ], 
      [ 0, 2, 1, 3, 2, 0 ], [ 0, 1, 1, 2, 2, 2 ], [ 1, 3, 2, 0, 2, 0 ] ] ]