degree:12
 order:54
[ 12, 8, 15, 18 ][ 12, 0, 2, 0, 0, 10 ]

minimal polynomial:[ x-12, x, x+12, x^2-90 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-7*x-8
x^5-315*x^3+20250*x
x^3-9*x^2-162*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, 8, 0, 3 ], [ 0, 12, 0, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 2, 0, 10, 0 ] ], 
  [ [ 0, 0, 8, 0, 0 ], [ 0, 8, 0, 0, 0 ], [ 1, 0, 7, 0, 0 ], [ 0, 0, 0, 8, 0 ], [ 0, 0, 0, 0, 8 ] ], 
  [ [ 0, 0, 0, 15, 0 ], [ 0, 0, 0, 0, 15 ], [ 0, 0, 0, 15, 0 ], [ 1, 0, 8, 0, 6 ], [ 0, 10, 0, 5, 0 ] ], 
  [ [ 0, 0, 0, 0, 18 ], [ 0, 3, 0, 15, 0 ], [ 0, 0, 0, 0, 18 ], [ 0, 12, 0, 6, 0 ], [ 1, 0, 8, 0, 9 ] ] ]