degree:12
 order:56
[ 12, 12, 3, 4, 24 ][ 1, 4, 6, 3, 8, 6, 3, 0, 0, 0 ]

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

 minimal polynomial of other basis elements:
 x^6-8*x^5-80*x^4+352*x^3+576*x^2-2304*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, 1, 1, 1, 2, 6 ], [ 0, 1, 1, 2, 2, 6 ], 
      [ 0, 4, 8, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 1, 2, 2, 6 ], [ 1, 1, 1, 1, 2, 6 ], 
      [ 0, 8, 4, 0, 0, 0 ], [ 0, 6, 6, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 3, 0, 0 ], [ 0, 1, 2, 0, 0, 0 ], [ 0, 2, 1, 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, 2, 2, 0, 0, 0 ], [ 0, 2, 2, 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 ] ] ]