degree:12
 order:36
[ 12, 3, 8, 12 ][ 12, 3, 0, 0, 0, 6 ]

minimal polynomial:[ x-12, x, x+6, x^2-6*x-36 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^3-4*x^2-32*x
x^5-144*x^3-216*x^2+2592*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, 3, 2, 0 ], [ 0, 12, 0, 0, 0 ], [ 0, 3, 0, 0, 9 ], [ 0, 0, 0, 6, 6 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 8, 0 ], [ 0, 2, 0, 0, 6 ], [ 0, 0, 0, 8, 0 ], [ 1, 0, 3, 4, 0 ], [ 0, 6, 0, 0, 2 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 6, 6 ], [ 0, 0, 0, 0, 12 ], [ 0, 9, 0, 0, 3 ], [ 1, 6, 3, 2, 0 ] ] ]