degree:12
 order:60
[ 12, 12, 15, 20 ][ 1, 0, 3, 4, 3, 3 ]

minimal polynomial:[ x-12, x, x+3, x^2-4*x-16 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^5-13*x^4-16*x^3+288*x^2+576*x
x^4-13*x^3-45*x^2+225*x
x^4-21*x^3+400*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, 12, 0, 0, 0 ], [ 1, 5, 1, 0, 5 ], [ 0, 1, 1, 5, 5 ], [ 0, 0, 4, 4, 4 ], [ 0, 3, 3, 3, 3 ] ], 
  [ [ 0, 0, 12, 0, 0 ], [ 0, 1, 1, 5, 5 ], [ 1, 1, 5, 0, 5 ], [ 0, 4, 0, 4, 4 ], [ 0, 3, 3, 3, 3 ] ], 
  [ [ 0, 0, 0, 15, 0 ], [ 0, 0, 5, 5, 5 ], [ 0, 5, 0, 5, 5 ], [ 1, 4, 4, 2, 4 ], [ 0, 3, 3, 3, 6 ] ], 
  [ [ 0, 0, 0, 0, 20 ], [ 0, 5, 5, 5, 5 ], [ 0, 5, 5, 5, 5 ], [ 0, 4, 4, 4, 8 ], [ 1, 3, 3, 6, 7 ] ] ]