degree:12
 order:44
[ 12, 1, 10, 20 ][ 12, 0, 6, 0, 0, 6 ]

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

 minimal polynomial of other basis elements:
 x^2-1
x^5-112*x^3+1200*x
x^3-18*x^2-40*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, 1, 0, 10 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 6, 0, 6, 0 ] ], 
  [ [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 10, 0 ], [ 0, 0, 0, 0, 10 ], [ 0, 0, 0, 10, 0 ], [ 1, 0, 1, 0, 8 ], [ 0, 6, 0, 4, 0 ] ], 
  [ [ 0, 0, 0, 0, 20 ], [ 0, 10, 0, 10, 0 ], [ 0, 0, 0, 0, 20 ], [ 0, 12, 0, 8, 0 ], [ 1, 0, 1, 0, 18 ] 
     ] ]