Group action invariants
| Degree $n$ : | $35$ | |
| Transitive number $t$ : | $45$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,23)(2,22)(3,26)(4,27)(5,24)(6,25)(7,28)(8,21,10,20,14,17,12,16,9,15,13,19,11,18)(29,34,33,31,32,30,35), (1,12)(2,8)(3,9)(4,14)(5,11)(6,10)(7,13)(15,31,16,33,17,34,20,29,21,35,18,30,19,32)(22,23)(24,26)(25,27) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 10: $D_{5}$ 20: $D_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $D_{5}$
Degree 7: None
Low degree siblings
35T45 x 15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 200 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $48020=2^{2} \cdot 5 \cdot 7^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |