Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $37$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| 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) |
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: | not available |
| Character table: not available. |