Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,5,7,2,4,6)(8,21,9,18,10,15,11,19,12,16,13,20,14,17), (1,10,15,6,8,16)(2,11,18,5,14,20)(3,12,21,4,13,17)(7,9,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 14: $D_{7}$ 28: $D_{14}$ 84: 21T8 588: 14T25 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
21T37 x 5, 42T392 x 6, 42T393 x 6, 42T394 x 6, 42T400 x 3, 42T401 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 79 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4116=2^{2} \cdot 3 \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |