degree:12
 order:48
[ 12, 7, 12, 16 ][ 12, 0, 3, 0, 0, 9 ]

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

 minimal polynomial of other basis elements:
 x^2-6*x-7
x^5-216*x^3+10368*x
x^3-8*x^2-128*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, 7, 0, 4 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 3, 0, 9, 0 ] ], 
  [ [ 0, 0, 7, 0, 0 ], [ 0, 7, 0, 0, 0 ], [ 1, 0, 6, 0, 0 ], [ 0, 0, 0, 7, 0 ], [ 0, 0, 0, 0, 7 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 7, 0, 4 ], [ 0, 9, 0, 3, 0 ] ], 
  [ [ 0, 0, 0, 0, 16 ], [ 0, 4, 0, 12, 0 ], [ 0, 0, 0, 0, 16 ], [ 0, 12, 0, 4, 0 ], [ 1, 0, 7, 0, 8 ] ] ]