Group action invariants
| Degree $n$ : | $39$ | |
| Transitive number $t$ : | $20$ | |
| Group : | $C_{13}:(C_{13}:C_3)$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,23,38)(2,20,39)(3,17,29)(4,19,36)(5,16,33)(6,24,32)(7,22,35)(8,15,31)(9,26,30)(10,18,34)(11,21,27)(12,14,37)(13,25,28), (1,22,32)(2,15,30)(3,18,31)(4,26,35)(5,20,36)(6,14,29)(7,21,37)(8,25,33)(9,16,27)(10,24,28)(11,19,38)(12,23,34)(13,17,39) | |
| $|\Aut(F/K)|$: | $13$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 39: $C_{13}:C_3$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T20 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 59 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $507=3 \cdot 13^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [507, 5] |
| Character table: Data not available. |