Group action invariants
| Degree $n$: | $39$ | |
| Transitive number $t$: | $21$ | |
| Group: | $C_{13}\times C_{13}:C_3$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $13$ | |
| Generators: | (1,28,22,11,35,20,9,31,24,2,38,19,13,39,25,10,37,23,12,33,16,7,32,18,4,30,21,5,34,15,8,36,14,3,29,26,6,27,17), (1,21,27,8,23,34,7,24,33,13,17,38,11,15,28,3,16,36,4,19,32,10,22,39,9,14,35,6,18,29,5,25,30,12,20,37,2,26,31) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $13$: $C_{13}$ $39$: $C_{13}:C_3$, $C_{39}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T21 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 91 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $507=3 \cdot 13^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [507, 3] |
| Character table: not available. |