degree:12
 order:60
[ 12, 8, 3, 12, 24 ][ 3, 12, 0, 3, 0, 6, 0, 0, 0, 3 ]

minimal polynomial:[ x-12, x-6, x, x+6, x^2+6*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-4*x^2-32*x
x^2-2*x-3
x^6-6*x^5-144*x^4+648*x^3+3888*x^2-15552*x
x^4-12*x^3-432*x^2+3456*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, 3, 0, 0, 9, 0 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 3, 0, 0, 3, 6 ] ], 
  [ [ 0, 0, 8, 0, 0, 0 ], [ 0, 2, 0, 0, 6, 0 ], [ 1, 0, 4, 3, 0, 0 ], 
      [ 0, 0, 8, 0, 0, 0 ], [ 0, 6, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 8 ] ], 
  [ [ 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, 12, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 9, 0, 0, 3, 0 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 0, 2, 3, 0, 6 ], [ 0, 3, 0, 0, 3, 6 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 6, 0, 0, 6, 12 ], [ 0, 0, 0, 0, 0, 24 ], 
      [ 0, 0, 0, 0, 0, 24 ], [ 0, 6, 0, 0, 6, 12 ], [ 1, 6, 8, 3, 6, 0 ] ] ]