Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $133$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,8,11,20,6)(2,13,7,10,19,5,3,15,9,12,21,4)(17,18), (1,9,3,8)(2,7)(4,5,6)(10,21,12,20)(11,19)(13,18)(14,17)(15,16) | |
| $|\Aut(F/K)|$: | $1$ |
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
42T2474, 42T2475, 42T2476, 42T2507Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 105 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. |