degree:12
 order:60
[ 12, 5, 18, 24 ][ 12, 0, 3, 0, 0, 9 ]

minimal polynomial:[ x-12, x, x+12, x^2-54 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-4*x-5
x^5-378*x^3+17496*x
x^3-18*x^2-144*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, 0, 5, 0, 6 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 0, 9, 0 ] ], 
  [ [ 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, 18, 0 ], [ 0, 0, 0, 0, 18 ], [ 0, 0, 0, 18, 0 ], [ 1, 0, 5, 0, 12 ], [ 0, 9, 0, 9, 0 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 0, 18, 0 ], [ 0, 0, 0, 0, 24 ], [ 0, 12, 0, 12, 0 ], [ 1, 0, 5, 0, 18 ] 
     ] ]