Group action invariants
| Degree $n$: | $35$ | |
| Transitive number $t$: | $43$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,15,29,11,22)(2,21,32,10,27)(3,16,34,12,26)(4,19,35,14,23)(5,20,31,9,28)(6,18,30,13,24)(7,17,33,8,25), (1,23,11,32,20,5,27,14,29,16,7,22,10,35,21)(2,26,12,34,18)(3,28,8,30,15,6,24,9,33,17,4,25,13,31,19) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $5$: $C_5$ $15$: $C_{15}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: None
Low degree siblings
35T43 x 79Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 175 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $36015=3 \cdot 5 \cdot 7^{4}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |