degree:12
 order:60
[ 12, 16, 1, 6, 24 ][ 6, 12, 0, 1, 0, 8, 2, 0, 0, 1 ]

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

 minimal polynomial of other basis elements:
 x^6-24*x^5+80*x^4+896*x^3-1536*x^2-8192*x
x^2-1
x^5-2*x^4-36*x^3+24*x^2+288*x
x^4-16*x^3-240*x^2+1152*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, 8, 1, 0, 2 ], [ 0, 6, 0, 0, 3, 3 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 8, 0, 0, 4 ], [ 0, 1, 2, 0, 1, 8 ] ], 
  [ [ 0, 0, 16, 0, 0, 0 ], [ 0, 8, 0, 0, 4, 4 ], [ 1, 0, 8, 1, 0, 6 ], 
      [ 0, 0, 16, 0, 0, 0 ], [ 0, 8, 0, 0, 0, 8 ], [ 0, 2, 4, 0, 2, 8 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 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, 6, 0 ], [ 0, 0, 4, 0, 0, 2 ], [ 0, 3, 0, 0, 0, 3 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 0, 4 ], [ 0, 1, 2, 0, 1, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 2, 4, 0, 2, 16 ], [ 0, 3, 6, 0, 3, 12 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 4, 8, 0, 4, 8 ], [ 1, 8, 8, 1, 2, 4 ] ] ]