Group action invariants
| Degree $n$: | $35$ | |
| Transitive number $t$: | $41$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $5$ | |
| Generators: | (1,21,6,26,16)(2,22,7,27,17)(3,23,8,28,18)(4,24,9,29,19)(5,25,10,30,20)(11,31)(12,32)(13,33)(14,34)(15,35), (1,14,22,20,8,31,29,2,15,23,16,9,32,30,3,11,24,17,10,33,26,4,12,25,18,6,34,27,5,13,21,19,7,35,28) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $10$: $C_{10}$ $5040$: $S_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: $S_7$
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 75 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25200=2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |