degree:12
 order:52
[ 12, 12, 1, 2, 24 ][ 2, 0, 6, 3, 12, 6, 3, 0, 0, 0 ]

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

 minimal polynomial of other basis elements:
 x^6-10*x^5-48*x^4+264*x^3+432*x^2-1728*x
x^2-1
x^3-4*x
x^4-20*x^3-144*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, 2, 2, 0, 1, 6 ], [ 0, 2, 2, 1, 1, 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, 2, 2, 1, 1, 6 ], [ 1, 2, 2, 0, 1, 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, 2, 0 ], [ 0, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 2, 0 ], [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], 
  [ [ 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, 2, 8 ] ] ]