Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $46$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,20,7,11,18,6,14,16,5,10,21,4,13,19,3,9,17,2,12,15), (1,5)(2,4)(6,7)(8,16,9,19)(10,15,14,20)(11,18,13,17)(12,21) | |
| $|\Aut(F/K)|$: | $1$ |
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
28T347, 42T538, 42T539, 42T540, 42T548Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8232=2^{3} \cdot 3 \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |