degree:12
 order:49
[ 12, 12, 12, 12 ][ 2, 3, 4, 4, 4, 1 ]

minimal polynomial:[ x-12, x+2, x^3-x^2-16*x+29 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^3-15*x^2+26*x+120
x^5-11*x^4-30*x^3+213*x^2+94*x-696
x^5-11*x^4-30*x^3+213*x^2+94*x-696

 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, 2, 2, 3, 4 ], [ 0, 2, 2, 4, 4 ], [ 0, 3, 4, 4, 1 ], [ 0, 4, 4, 1, 3 ] ], 
  [ [ 0, 0, 12, 0, 0 ], [ 0, 2, 2, 4, 4 ], [ 1, 2, 5, 2, 2 ], [ 0, 4, 2, 2, 4 ], [ 0, 4, 2, 4, 2 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 3, 4, 4, 1 ], [ 0, 4, 2, 2, 4 ], [ 1, 4, 2, 2, 3 ], [ 0, 1, 4, 3, 4 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 4, 4, 1, 3 ], [ 0, 4, 2, 4, 2 ], [ 0, 1, 4, 3, 4 ], [ 1, 3, 2, 4, 2 ] ] ]