degree:6
 order:40
[ 6, 12, 1, 8, 12 ][ 2, 6, 0, 0, 0, 3, 1, 0, 0, 2 ]

minimal polynomial:[ x-6, x, x+2, x^3-18*x+12 ]
 Galois type:2

 minimal polynomial of other basis elements:
 x^6-8*x^5-75*x^4+252*x^3+1008*x^2-1728*x
x^2-1
x^3-6*x^2-16*x
x^6-8*x^5-75*x^4+222*x^3+1248*x^2-288*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, 6, 0, 0, 0, 0 ], [ 1, 0, 4, 1, 0, 0 ], [ 0, 2, 1, 0, 2, 1 ], 
      [ 0, 6, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0, 3 ], [ 0, 0, 1, 0, 2, 3 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 4, 2, 0, 4, 2 ], [ 1, 1, 2, 1, 2, 5 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 6 ], [ 0, 1, 5, 0, 4, 2 ] ], 
  [ [ 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, 8, 0 ], [ 0, 0, 4, 0, 0, 4 ], [ 0, 2, 2, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 8, 0 ], [ 1, 0, 0, 1, 6, 0 ], [ 0, 2, 4, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 0, 12 ], [ 0, 0, 2, 0, 4, 6 ], [ 0, 1, 5, 0, 4, 2 ], 
      [ 0, 0, 0, 0, 0, 12 ], [ 0, 3, 6, 0, 0, 3 ], [ 1, 3, 2, 1, 2, 3 ] ] ]