degree:12
 order:35
[ 12, 4, 6, 12 ][ 3, 4, 5, 2, 1, 3 ]

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

 minimal polynomial of other basis elements:
 x^5-3*x^4-10*x^3+20*x^2+18*x-8
x^2-5*x-6
x^5-9*x^4-48*x^3+106*x^2+450*x+72

 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, 12, 0, 0, 0 ], [ 1, 3, 1, 2, 5 ], [ 0, 3, 3, 3, 3 ], [ 0, 4, 2, 0, 6 ], [ 0, 5, 1, 3, 3 ] ], 
  [ [ 0, 0, 4, 0, 0 ], [ 0, 1, 1, 1, 1 ], [ 1, 3, 0, 0, 0 ], [ 0, 2, 0, 0, 2 ], [ 0, 1, 0, 1, 2 ] ], 
  [ [ 0, 0, 0, 6, 0 ], [ 0, 2, 1, 0, 3 ], [ 0, 3, 0, 0, 3 ], [ 1, 0, 0, 5, 0 ], [ 0, 3, 1, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 5, 1, 3, 3 ], [ 0, 3, 0, 3, 6 ], [ 0, 6, 2, 0, 4 ], [ 1, 3, 2, 2, 4 ] ] ]