degree:12
 order:54
[ 12, 1, 16, 24 ][ 12, 3, 0, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x+6, x^2-6*x-18 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^3-14*x^2-32*x
x^5-6*x^4-378*x^3-1512*x^2+5184*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, 1, 4, 0 ], [ 0, 12, 0, 0, 0 ], 
      [ 0, 3, 0, 0, 9 ], [ 0, 0, 0, 6, 6 ] ], 
  [ [ 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, 16, 0 ], [ 0, 4, 0, 0, 12 ], [ 0, 0, 0, 16, 0 ], 
      [ 1, 0, 1, 14, 0 ], [ 0, 6, 0, 0, 10 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 0, 0, 12, 12 ], [ 0, 0, 0, 0, 24 ], 
      [ 0, 9, 0, 0, 15 ], [ 1, 6, 1, 10, 6 ] ] ]