Group action invariants
| Degree $n$ : | $35$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,31,11,26)(2,17,29,10,24)(3,19,32,12,25)(4,21,33,14,22)(5,16,35,9,27)(6,20,34,13,23)(7,15,30,8,28), (1,28,9,34,16,3,25,10,29,17)(2,23,11,32,18)(4,27,8,33,15,7,26,13,35,20)(5,22,14,30,21,6,24,12,31,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 10: $C_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: None
Low degree siblings
35T37 x 79Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 250 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. |