Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $152$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,6,2,16,5,3,17,4)(7,20,9,19,8,21)(10,11), (1,20,6,9,13,3,21,5,8,15,2,19,4,7,14)(10,17,12,18,11,16) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5040: $S_7$ 10080: $S_7\times C_2$ 322560: 14T54 645120: 14T57 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
42T5388, 42T5389, 42T5390, 42T5391, 42T5392, 42T5393, 42T5394Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 429 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1410877440=2^{11} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |