Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $122$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18)(2,16)(3,17)(4,13,5,14,6,15)(7,12)(8,10)(9,11)(19,21,20), (1,21,3,20)(2,19)(4,17,5,16,6,18)(7,13,8,14,9,15)(11,12) | |
| $|\Aut(F/K)|$: | $1$ |
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
42T2096 x 3, 42T2097 x 3, 42T2098, 42T2099 x 3, 42T2100, 42T2101 x 3, 42T2102, 42T2139 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 171 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. |