degree:6
 order:55
[ 6, 12, 12, 12, 12 ][ 1, 1, 0, 0, 1, 0, 2, 2, 2, 2 ]

minimal polynomial:[ x-6, x+3, x^2-2*x-4, x^2-3 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^4-6*x^3-75*x^2+10*x+312
x^5-11*x^4-34*x^3+268*x^2-32*x-192
x^6-11*x^5-35*x^4+264*x^3+276*x^2-1584*x
x^6-11*x^5-37*x^4+244*x^3+664*x^2+128*x-384

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