degree:12
 order:48
[ 12, 4, 1, 6, 24 ][ 6, 12, 0, 4, 0, 4, 0, 0, 0, 2 ]

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

 minimal polynomial of other basis elements:
 x^3-2*x^2-8*x
x^2-1
x^6-3*x^5-36*x^4+72*x^3+288*x^2-432*x
x^4-21*x^3-144*x^2+1728*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, 1, 0, 8 ], [ 0, 6, 0, 0, 6, 0 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 8 ], [ 0, 4, 0, 0, 2, 6 ] ], 
  [ [ 0, 0, 4, 0, 0, 0 ], [ 0, 2, 0, 0, 2, 0 ], [ 1, 0, 2, 1, 0, 0 ], 
      [ 0, 0, 4, 0, 0, 0 ], [ 0, 4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 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, 6, 0 ], [ 0, 0, 2, 0, 0, 4 ], [ 0, 6, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 0, 6, 0 ], [ 1, 0, 0, 1, 0, 4 ], [ 0, 2, 0, 0, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 8, 0, 0, 4, 12 ], [ 0, 0, 0, 0, 0, 24 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 8, 0, 0, 4, 12 ], [ 1, 6, 4, 1, 3, 9 ] ] ]