Group action invariants
| Degree $n$: | $39$ | |
| Transitive number $t$: | $48$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $13$ | |
| Generators: | (1,27,22,2,30,20,12,39,24,5,28,19,6,34,25,9,37,23,10,35,16,4,36,18,3,33,21,11,31,15,13,29,14,7,32,26,8,38,17), (1,36,19,2,33,25,12,31,23,5,29,16,6,32,18,9,38,21,10,27,15,4,30,14,3,39,26,11,28,17,13,34,22,7,37,20,8,35,24) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $13$: $C_{13}$ $39$: $C_{13}:C_3$ x 2, $C_{39}$ $507$: 39T20, 39T21 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T48 x 47Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 767 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6591=3 \cdot 13^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |