Group action invariants
| Degree $n$ : | $35$ | |
| Transitive number $t$ : | $38$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,35,2,31,3,29,6,32,7,34,4,30,5,33)(8,28,12,27,11,24,14,23,13,22,10,26,9,25)(15,19,18,21,20,17,16), (1,7,2,4,3,5,6)(8,35,12,31,11,29,14,32,13,34,10,30,9,33)(15,23,16,26,17,28,20,24,21,22,18,25,19,27) | |
| $|\Aut(F/K)|$: | $7$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 10: $D_{5}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $D_{5}$
Degree 7: None
Low degree siblings
35T38 x 7, 35T39 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 316 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $24010=2 \cdot 5 \cdot 7^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |