degree:12
 order:42
[ 12, 5, 12, 12 ][ 12, 0, 4, 0, 0, 8 ]

minimal polynomial:[ x-12, x, x^3+6*x^2-72*x-384 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-4*x-5
x^5-6*x^4-144*x^3+480*x^2+4608*x
x^5-6*x^4-144*x^3+480*x^2+4608*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, 4, 8 ], [ 0, 4, 0, 8, 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, 12, 0 ], [ 0, 0, 0, 4, 8 ], [ 0, 0, 0, 12, 0 ], [ 1, 4, 5, 2, 0 ], [ 0, 8, 0, 0, 4 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 4, 0, 8, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 8, 0, 0, 4 ], [ 1, 0, 5, 4, 2 ] ] ]