degree:12
 order:45
[ 12, 4, 4, 24 ][ 6, 0, 3, 0, 1, 2 ]

minimal polynomial:[ x-12, x, x+3, x^2-18 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-3*x^2-6*x+8
x^3-3*x^2-6*x+8
x^5-18*x^4-162*x^3+324*x^2+2592*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, 3, 2, 0, 6 ], [ 0, 6, 0, 0, 6 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 1, 2, 6 ] ], 
  [ [ 0, 0, 4, 0, 0 ], [ 0, 2, 0, 0, 2 ], [ 1, 0, 1, 2, 0 ], [ 0, 0, 2, 2, 0 ], [ 0, 1, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 2, 2, 0 ], [ 1, 0, 2, 1, 0 ], [ 0, 2, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 2, 4, 12 ], [ 0, 6, 0, 0, 18 ], [ 0, 12, 0, 0, 12 ], [ 1, 6, 3, 2, 12 ] 
     ] ]