degree:12
 order:40
[ 12, 3, 12, 12 ][ 12, 0, 2, 0, 0, 8 ]

minimal polynomial:[ x-12, x, x+4, x^2-4*x-56 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^4-8*x^3-80*x^2+384*x
x^5-12*x^4-72*x^3+640*x^2+2688*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, 6, 3, 0, 2 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 4, 8 ], [ 0, 2, 0, 8, 2 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 4, 8 ], [ 0, 0, 0, 12, 0 ], [ 1, 4, 3, 0, 4 ], [ 0, 8, 0, 4, 0 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 2, 0, 8, 2 ], [ 0, 0, 0, 0, 12 ], [ 0, 8, 0, 4, 0 ], [ 1, 2, 3, 0, 6 ] ] ]