Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $45$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,9,6,20,11)(2,19,8,5,18,12)(3,21,14,4,16,13)(7,15,10), (1,5,2,6,3,7,4)(8,13,11,9,14,12,10)(15,19)(16,18)(20,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
28T349, 28T350 x 2, 42T533, 42T534, 42T535 x 2, 42T536 x 2, 42T537, 42T545 x 2, 42T546Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 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. |