degree:12
 order:54
[ 12, 5, 12, 24 ][ 12, 0, 2, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x+6, x^2-72 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-4*x-5
x^3-6*x^2-72*x
x^5-12*x^4-360*x^3+864*x^2+20736*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, 2, 5, 0, 4 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 2, 0, 6, 4 ] ], 
  [ [ 0, 0, 5, 0, 0 ], [ 0, 5, 0, 0, 0 ], [ 1, 0, 4, 0, 0 ], [ 0, 0, 0, 5, 0 ], [ 0, 0, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 5, 6, 0 ], [ 0, 6, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 4, 0, 12, 8 ], [ 0, 0, 0, 0, 24 ], [ 0, 12, 0, 0, 12 ], [ 1, 4, 5, 6, 8 ] ] 
 ]