Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $124$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,21,7,17,6,14,2,12,19,9,18,5,13,3,11,20,8,16,4,15), (1,20,3,19)(2,21)(4,16,5,18)(6,17)(7,13)(8,15,9,14)(10,12,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 14: $D_{7}$ 896: 14T27 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
42T2130 x 3, 42T2131 x 3, 42T2132 x 3, 42T2133, 42T2134 x 3, 42T2135, 42T2136, 42T2138 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 168 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1959552=2^{7} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |