degree:12
 order:38
[ 12, 1, 12, 12 ][ 12, 4, 2, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x^3+2*x^2-24*x-56 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^5-10*x^4-48*x^3+232*x^2+672*x
x^5-10*x^4-48*x^3+232*x^2+672*x

 SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], 
      [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0 ], [ 1, 4, 1, 4, 2 ], [ 0, 12, 0, 0, 0 ], 
      [ 0, 4, 0, 2, 6 ], [ 0, 2, 0, 6, 4 ] ], 
  [ [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 4, 0, 2, 6 ], [ 0, 0, 0, 12, 0 ], 
      [ 1, 2, 1, 4, 4 ], [ 0, 6, 0, 4, 2 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 2, 0, 6, 4 ], [ 0, 0, 0, 0, 12 ], 
      [ 0, 6, 0, 4, 2 ], [ 1, 4, 1, 2, 4 ] ] ]