degree:12
 order:55
[ 12, 6, 4, 8, 24 ][ 4, 3, 3, 2, 0, 3, 1, 0, 1, 2 ]

minimal polynomial:[ x-12, x, x^2-12, x^2+x-11 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-5*x^5-19*x^4+63*x^3+120*x^2-144*x-216
x^6-3*x^5-13*x^4+30*x^3+38*x^2-60*x+16
x^4-12*x^3+26*x^2+60*x-96
x^6-22*x^5-82*x^4+720*x^3+2352*x^2-1008*x-3456

 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, 2, 2, 1, 2, 4 ], [ 0, 4, 0, 0, 4, 4 ], 
      [ 0, 3, 0, 3, 0, 6 ], [ 0, 3, 3, 0, 0, 6 ], [ 0, 2, 1, 1, 2, 6 ] ], 
  [ [ 0, 0, 6, 0, 0, 0 ], [ 0, 2, 0, 0, 2, 2 ], [ 1, 0, 1, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 0, 6 ], [ 0, 3, 0, 0, 0, 3 ], [ 0, 1, 1, 1, 1, 2 ] ], 
  [ [ 0, 0, 0, 4, 0, 0 ], [ 0, 1, 0, 1, 0, 2 ], [ 0, 0, 0, 0, 0, 4 ], 
      [ 1, 3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 3 ], [ 0, 1, 1, 0, 1, 1 ] ], 
  [ [ 0, 0, 0, 0, 8, 0 ], [ 0, 2, 2, 0, 0, 4 ], [ 0, 4, 0, 0, 0, 4 ], 
      [ 0, 0, 0, 0, 2, 6 ], [ 1, 0, 0, 1, 3, 3 ], [ 0, 2, 1, 1, 1, 3 ] ], 
  [ [ 0, 0, 0, 0, 0, 24 ], [ 0, 4, 2, 2, 4, 12 ], [ 0, 4, 4, 4, 4, 8 ], 
      [ 0, 6, 6, 0, 6, 6 ], [ 0, 6, 3, 3, 3, 9 ], [ 1, 6, 2, 1, 3, 11 ] ] ]