degree:12
 order:42
[ 12, 5, 12, 12 ][ 12, 0, 6, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x^3+6*x^2-72*x-216 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-4*x-5
x^5-6*x^4-144*x^3+648*x^2+2592*x
x^5-6*x^4-144*x^3+648*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, 0, 5, 0, 6 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 6, 6 ], [ 0, 6, 0, 6, 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, 6, 6 ], [ 0, 0, 0, 12, 0 ], [ 1, 6, 5, 0, 0 ], [ 0, 6, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 6, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 0, 6 ], [ 1, 0, 5, 6, 0 ] ] ]