degree:12
 order:60
[ 12, 12, 1, 4, 30 ][ 4, 0, 6, 2, 12, 6, 2, 0, 0, 0 ]

minimal polynomial:[ x-12, x-2, x, x+6, x^2-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-16*x^5+12*x^4+528*x^3-864*x^2-3456*x
x^2-1
x^3-2*x^2-8*x
x^4-18*x^3-420*x^2+1800*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, 4, 0, 2, 5 ], [ 0, 4, 0, 1, 2, 5 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 8 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 1, 2, 5 ], [ 1, 0, 4, 0, 2, 5 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 8 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 4, 0 ], [ 0, 2, 2, 0, 0, 0 ], [ 0, 2, 2, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 1, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 30 ], [ 0, 5, 5, 0, 0, 20 ], [ 0, 5, 5, 0, 0, 20 ], 
      [ 0, 0, 0, 0, 0, 30 ], [ 0, 0, 0, 0, 0, 30 ], [ 1, 8, 8, 1, 4, 8 ] ] ]