Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $161$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,2,13,7,10,5,14)(3,8,4,9,6,12)(15,16,21)(17,19,20), (1,14,18,3,10,20,6,13,21,4,8,17,5,11,16)(2,12,19)(7,9,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 24: $S_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
42T7900, 42T7901, 42T7902Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 472 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $384072192000=2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |