degree:10
 order:57
[ 10, 10, 6, 30 ][ 2, 0, 2, 5, 1, 1 ]

minimal polynomial:[ x-10, x^2-5, x^2+x-14 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^5-9*x^4-29*x^3+185*x^2+120*x-700
x^4-6*x^3-8*x^2+51*x-18
x^4-28*x^3-80*x^2+615*x-450

 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, 10, 0, 0, 0 ], [ 1, 1, 2, 0, 6 ], [ 0, 2, 2, 3, 3 ], [ 0, 0, 5, 0, 5 ], [ 0, 2, 1, 1, 6 ] ], 
  [ [ 0, 0, 10, 0, 0 ], [ 0, 2, 2, 3, 3 ], [ 1, 2, 1, 0, 6 ], [ 0, 5, 0, 0, 5 ], [ 0, 1, 2, 1, 6 ] ], 
  [ [ 0, 0, 0, 6, 0 ], [ 0, 0, 3, 0, 3 ], [ 0, 3, 0, 0, 3 ], [ 1, 0, 0, 0, 5 ], [ 0, 1, 1, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 30 ], [ 0, 6, 3, 3, 18 ], [ 0, 3, 6, 3, 18 ], [ 0, 5, 5, 5, 15 ], [ 1, 6, 6, 3, 14 ] ] ]