Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $115$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,2)(4,21,13,5,20,14,6,19,15)(7,17,12,9,16,10,8,18,11), (1,17,5,13,21,8,12,3,16,6,14,20,7,10,2,18,4,15,19,9,11) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 168: $\GL(3,2)$ 504: 21T22 122472: 21T104 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
21T115 x 3, 42T1636 x 4, 42T1641 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 228 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $367416=2^{3} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |