Group action invariants
| Degree $n$ : | $35$ | |
| Transitive number $t$ : | $49$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,16,34,6,24,11,4,26,19,31,9,21,14)(2,28,17,33,7,23,12,3,27,18,32,8,22,13)(5,30,20,35,10,25,15), (1,33,6,23,11,3,31,8,21,13)(2,32,7,22,12)(4,35,9,25,14,5,34,10,24,15)(16,28)(17,27)(18,26)(19,30)(20,29) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 10: $D_{5}$ 20: $D_{10}$ 5040: $S_7$ 10080: $S_7\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $D_{5}$
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 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $50400=2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |