degree:12
 order:56
[ 12, 12, 3, 4, 24 ][ 2, 12, 0, 3, 0, 12, 3, 0, 0, 0 ]

minimal polynomial:[ x-12, x-6, x, x+8, x^2+4*x-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-10*x^5-104*x^4+816*x^3+2880*x^2-13824*x
x^2-2*x-3
x^3-16*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, 0, 2, 3, 0, 6 ], [ 0, 2, 0, 0, 4, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 12, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 2, 0, 0, 4, 6 ], [ 1, 0, 2, 3, 0, 6 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 12, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 0 ], 
      [ 1, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 4, 0 ], [ 0, 0, 4, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], 
  [ [ 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, 3, 4, 4 ] ] ]