Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $134$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,9,5,12,19,3,18,7,6,10,20)(2,17,8,4,11,21)(13,14,15), (1,11,13,8,21,16,3,12,14,7,20,17)(2,10,15,9,19,18) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 42: $F_7$ 2688: 14T40 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $F_7$
Low degree siblings
42T2477, 42T2478, 42T2479, 42T2506Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 96 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5878656=2^{7} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |