degree:12
 order:42
[ 12, 12, 1, 4, 12 ][ 4, 12, 0, 2, 0, 6, 6, 0, 0, 2 ]

minimal polynomial:[ x-12, x, x+2, x+6, x^2-2*x-20 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-10*x^2-24*x
x^2-1
x^3-2*x^2-8*x
x^6-6*x^5-96*x^4+104*x^3+1968*x^2+2880*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, 4, 4, 1, 0, 2 ], [ 0, 4, 0, 0, 2, 6 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 6 ], [ 0, 2, 6, 0, 2, 2 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 0, 0, 2, 6 ], [ 1, 0, 10, 1, 0, 0 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 6, 0, 0, 0, 6 ], [ 0, 6, 0, 0, 2, 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, 4, 0 ], [ 0, 0, 2, 0, 0, 2 ], [ 0, 2, 0, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 4, 0 ], [ 1, 0, 0, 1, 2, 0 ], [ 0, 2, 2, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 2, 6, 0, 2, 2 ], [ 0, 6, 0, 0, 2, 4 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 6, 6, 0, 0, 0 ], [ 1, 2, 4, 1, 0, 4 ] ] ]