Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $62$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,6,21,4,19,2,17,7,15,5,20,3,18)(8,10,12,14,9,11,13), (1,9,5,10)(2,11,4,8)(3,13)(6,12,7,14)(15,20,18,16,21,19,17) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ 48: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
28T414, 42T707, 42T708, 42T709, 42T710, 42T711, 42T712, 42T713, 42T714Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $16464=2^{4} \cdot 3 \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |