Group action invariants
| Degree $n$: | $35$ | |
| Transitive number $t$: | $39$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,8,4,11,6,13,2,9,5,12,7,14,3,10)(15,34,18,31,20,30,16,29,19,33,21,32,17,35)(22,28)(23,27)(25,26), (1,17,29,13,25)(2,19,32,10,28)(3,20,34,9,27)(4,16,35,11,22)(5,18,31,14,26)(6,15,30,8,24)(7,21,33,12,23) |
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 8, 35T39 x 7Siblings 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: | not available |
| Character table: not available. |