Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $149$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,21,10)(2,15,20,12,3,13,19,11)(4,5,6)(8,9)(16,17,18), (1,13,6,16,2,15,4,18,3,14,5,17)(7,21,12,9,19,11,8,20,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5040: $S_7$ 322560: 14T54 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
42T4976, 42T4977, 42T4978Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 261 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $705438720=2^{10} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |