degree:12
 order:56
[ 12, 12, 1, 6, 24 ][ 1, 0, 6, 3, 12, 6, 3, 0, 0, 0 ]

minimal polynomial:[ x-12, x, x^2-12, x^2+4*x-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-8*x^5-84*x^4+384*x^3+864*x^2-3456*x
x^2-1
x^3-4*x^2-12*x
x^4-16*x^3-288*x^2+2304*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, 1, 1, 0, 3, 6 ], [ 0, 1, 1, 1, 3, 6 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 1, 1, 3, 6 ], [ 1, 1, 1, 0, 3, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 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, 6, 0 ], [ 0, 3, 3, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 4, 0 ], [ 0, 0, 0, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 6, 6, 0, 0, 12 ], [ 0, 6, 6, 0, 0, 12 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 0, 0, 24 ], [ 1, 6, 6, 1, 6, 4 ] ] ]