degree:10
 order:44
[ 10, 1, 12, 20 ][ 10, 0, 4, 0, 0, 6 ]

minimal polynomial:[ x-10, x, x+10, x^2-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^5-156*x^3+1728*x
x^3-18*x^2-40*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, 0, 1, 0, 8 ], [ 0, 10, 0, 0, 0 ], [ 0, 0, 0, 0, 10 ], [ 0, 4, 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, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 1, 0, 10 ], [ 0, 6, 0, 6, 0 ] ], 
  [ [ 0, 0, 0, 0, 20 ], [ 0, 8, 0, 12, 0 ], [ 0, 0, 0, 0, 20 ], [ 0, 10, 0, 10, 0 ], [ 1, 0, 1, 0, 18 ] ] ]