degree:6
 order:31
[ 6, 6, 6, 6, 6 ][ 2, 1, 0, 0, 2, 1, 1, 1, 2, 2 ]

minimal polynomial:[ x-6, x^5+x^4-12*x^3-21*x^2+x+5 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-5*x^5-18*x^4+51*x^3+127*x^2-x-30
x^6-5*x^5-18*x^4+51*x^3+127*x^2-x-30
x^6-5*x^5-18*x^4+51*x^3+127*x^2-x-30
x^6-5*x^5-18*x^4+51*x^3+127*x^2-x-30

 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, 2, 2, 1, 0, 0 ], [ 0, 2, 0, 2, 1, 1 ], 
      [ 0, 1, 2, 0, 1, 2 ], [ 0, 0, 1, 1, 2, 2 ], [ 0, 0, 1, 2, 2, 1 ] ], 
  [ [ 0, 0, 6, 0, 0, 0 ], [ 0, 2, 0, 2, 1, 1 ], [ 1, 0, 2, 0, 1, 2 ], 
      [ 0, 2, 0, 1, 2, 1 ], [ 0, 1, 1, 2, 0, 2 ], [ 0, 1, 2, 1, 2, 0 ] ], 
  [ [ 0, 0, 0, 6, 0, 0 ], [ 0, 1, 2, 0, 1, 2 ], [ 0, 2, 0, 1, 2, 1 ], 
      [ 1, 0, 1, 2, 2, 0 ], [ 0, 1, 2, 2, 0, 1 ], [ 0, 2, 1, 0, 1, 2 ] ], 
  [ [ 0, 0, 0, 0, 6, 0 ], [ 0, 0, 1, 1, 2, 2 ], [ 0, 1, 1, 2, 0, 2 ], 
      [ 0, 1, 2, 2, 0, 1 ], [ 1, 2, 0, 0, 2, 1 ], [ 0, 2, 2, 1, 1, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 6 ], [ 0, 0, 1, 2, 2, 1 ], [ 0, 1, 2, 1, 2, 0 ], 
      [ 0, 2, 1, 0, 1, 2 ], [ 0, 2, 2, 1, 1, 0 ], [ 1, 1, 0, 2, 0, 2 ] ] ]