degree:12
 order:52
[ 12, 3, 12, 24 ][ 4, 1, 3, 2, 0, 3 ]

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

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^5-8*x^4-64*x^3+152*x^2+576*x-1152
x^4-20*x^3-144*x^2+1152*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, 1, 1, 6 ], [ 0, 4, 0, 8, 0 ], [ 0, 1, 2, 3, 6 ], [ 0, 3, 0, 3, 6 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 1, 0, 2, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 2, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 1, 2, 3, 6 ], [ 0, 8, 0, 4, 0 ], [ 1, 3, 1, 1, 6 ], [ 0, 3, 0, 3, 6 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 6, 0, 6, 12 ], [ 0, 0, 0, 0, 24 ], [ 0, 6, 0, 6, 12 ], [ 1, 6, 3, 6, 8 ] ] ]