degree:6
 order:40
[ 6, 3, 6, 12, 12 ][ 2, 0, 2, 0, 2, 0, 0, 0, 2, 2 ]

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

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^6-4*x^5-32*x^4+96*x^3+240*x^2-576*x
x^5-12*x^4-20*x^3+240*x^2+64*x-768
x^3-10*x^2-32*x+96

 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, 6, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 4, 0 ], [ 0, 2, 0, 4, 0, 0 ], 
      [ 0, 0, 2, 0, 0, 4 ], [ 0, 2, 0, 0, 2, 2 ], [ 0, 0, 0, 2, 2, 2 ] ], 
  [ [ 0, 0, 3, 0, 0, 0 ], [ 0, 1, 0, 2, 0, 0 ], [ 1, 0, 2, 0, 0, 0 ], 
      [ 0, 2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 2 ], [ 0, 0, 0, 0, 2, 1 ] ], 
  [ [ 0, 0, 0, 6, 0, 0 ], [ 0, 0, 2, 0, 0, 4 ], [ 0, 4, 0, 2, 0, 0 ], 
      [ 1, 0, 1, 0, 4, 0 ], [ 0, 0, 0, 2, 2, 2 ], [ 0, 2, 0, 0, 2, 2 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 4, 0, 0, 4, 4 ], [ 0, 0, 0, 0, 4, 8 ], 
      [ 0, 0, 0, 4, 4, 4 ], [ 1, 2, 1, 2, 4, 2 ], [ 0, 2, 2, 2, 2, 4 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 0, 4, 4, 4 ], [ 0, 0, 0, 0, 8, 4 ], 
      [ 0, 4, 0, 0, 4, 4 ], [ 0, 2, 2, 2, 2, 4 ], [ 1, 2, 1, 2, 4, 2 ] ] ]