degree:12
 order:56
[ 12, 1, 18, 24 ][ 12, 4, 0, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x+2, x^2-48 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-1
x^5-27*x^4+114*x^3+828*x^2+648*x
x^4-19*x^3-144*x^2+576*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, 4, 1, 6, 0 ], [ 0, 12, 0, 0, 0 ], 
      [ 0, 4, 0, 0, 8 ], [ 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, 18, 0 ], [ 0, 6, 0, 0, 12 ], [ 0, 0, 0, 18, 0 ], 
      [ 1, 0, 1, 12, 4 ], [ 0, 6, 0, 3, 9 ] ], 
  [ [ 0, 0, 0, 0, 24 ], [ 0, 0, 0, 12, 12 ], [ 0, 0, 0, 0, 24 ], 
      [ 0, 8, 0, 4, 12 ], [ 1, 6, 1, 9, 7 ] ] ]