Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $130$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,4,12,7,21,13)(2,17,5,10,8,20,14)(3,18,6,11,9,19,15), (1,15,19,4,12,8,2,13,21,5,10,9,3,14,20,6,11,7)(16,18,17) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5040: $S_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
42T2268Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 143 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3674160=2^{4} \cdot 3^{8} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |