Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $118$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,12,7,14,17,4,3,19,10,9,15,18,6)(2,21,11,8,13,16,5), (1,4,19)(2,6,21,3,5,20)(7,10,17,9,11,18)(8,12,16)(14,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 168: $\GL(3,2)$ 336: 14T17 1008: 21T27 244944: 21T111 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
21T118 x 3, 42T1831 x 4, 42T1832 x 4, 42T1833 x 4, 42T1843 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 132 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $734832=2^{4} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |