Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $160$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,5)(4,6)(8,15,11,20,10,18,12,21,13,16,9,17)(14,19), (1,19)(2,18,3,17)(4,20,7,15)(5,21,6,16)(9,10,12,13,14,11) | |
| $|\Aut(F/K)|$: | $1$ |
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
42T7897, 42T7898, 42T7899Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 475 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. |