Group action invariants
| Degree $n$: | $35$ | |
| Transitive number $t$: | $33$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $7$ | |
| Generators: | (1,26,13,29,19)(2,24,8,32,20)(3,25,14,34,15)(4,22,10,35,18)(5,27,12,31,17)(6,23,9,30,21)(7,28,11,33,16), (1,6,5,3,4,2,7)(8,10,14,12,9,13,11)(15,17,21,19,16,20,18)(29,30,31,34,35,32,33) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $5$: $C_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: None
Low degree siblings
35T33 x 79Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 485 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $12005=5 \cdot 7^{4}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [12005, 16] |
| Character table: not available. |