degree:12
 order:56
[ 12, 12, 1, 12, 18 ][ 2, 12, 1, 0, 0, 4, 4, 0, 0, 4 ]

minimal polynomial:[ x-12, x, x+2, x+4, x^2-6*x-26 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-10*x^2-24*x
x^2-1
x^6-12*x^5-54*x^4+444*x^3+2240*x^2+2496*x
x^4-16*x^3-60*x^2+432*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, 7, 2, 1, 1, 0 ], [ 0, 2, 0, 0, 4, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 1, 4, 0, 1, 6 ], [ 0, 0, 4, 0, 4, 4 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 2, 0, 0, 4, 6 ], [ 1, 0, 10, 1, 0, 0 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 2, 6 ], [ 0, 4, 0, 0, 4, 4 ] ], 
  [ [ 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, 12, 0 ], [ 0, 1, 4, 0, 1, 6 ], [ 0, 4, 0, 0, 2, 6 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 1, 2, 1, 7, 0 ], [ 0, 4, 4, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 0, 6, 0, 6, 6 ], [ 0, 6, 0, 0, 6, 6 ], 
      [ 0, 0, 0, 0, 0, 18 ], [ 0, 6, 6, 0, 0, 6 ], [ 1, 4, 4, 1, 4, 4 ] ] ]