degree:10
 order:42
[ 10, 1, 10, 20 ][ 10, 1, 2, 0, 0, 4 ]

minimal polynomial:[ x-10, x, x+4, x^2-2*x-14 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^5-8*x^4-42*x^3+164*x^2+560*x
x^4-22*x^3+16*x^2+480*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, 10, 0, 0, 0 ], [ 1, 3, 1, 1, 4 ], [ 0, 10, 0, 0, 0 ], [ 0, 1, 0, 1, 8 ], [ 0, 2, 0, 4, 4 ] ], 
  [ [ 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, 10, 0 ], [ 0, 1, 0, 1, 8 ], [ 0, 0, 0, 10, 0 ], [ 1, 1, 1, 3, 4 ], [ 0, 4, 0, 2, 4 ] ], 
  [ [ 0, 0, 0, 0, 20 ], [ 0, 4, 0, 8, 8 ], [ 0, 0, 0, 0, 20 ], [ 0, 8, 0, 4, 8 ], [ 1, 4, 1, 4, 10 ] ] ]