degree:12
 order:60
[ 12, 24, 1, 10, 12 ][ 3, 0, 6, 0, 0, 0, 6, 0, 1, 5 ]

minimal polynomial:[ x-12, x, x^2-12, x^2+6*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-12*x^3-432*x^2+3456*x
x^2-1
x^3-8*x^2-20*x
x^6-6*x^5-120*x^4+504*x^3+1296*x^2-5184*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 0, 6, 0, 5, 0 ], [ 0, 3, 6, 0, 0, 3 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 0, 0, 0, 6 ], [ 0, 0, 6, 1, 5, 0 ] ], 
  [ [ 0, 0, 24, 0, 0, 0 ], [ 0, 6, 12, 0, 0, 6 ], [ 1, 6, 0, 1, 10, 6 ], 
      [ 0, 0, 24, 0, 0, 0 ], [ 0, 0, 24, 0, 0, 0 ], [ 0, 6, 12, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 10, 0 ], [ 0, 5, 0, 0, 0, 5 ], [ 0, 0, 10, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 10, 0 ], [ 1, 0, 0, 1, 8, 0 ], [ 0, 5, 0, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 6, 1, 5, 0 ], [ 0, 3, 6, 0, 0, 3 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 6 ], [ 1, 0, 6, 0, 5, 0 ] ] ]