Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $137$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,14,19,6,10,18)(2,8,15,21,4,12,17,3,7,13,20,5,11,16), (1,21,9,2,20,8)(3,19,7)(4,12,14,5,11,13)(6,10,15)(16,18,17) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 21: $C_7:C_3$ 42: $(C_7:C_3) \times C_2$ 168: $C_2^3:(C_7: C_3)$ x 2 336: 14T18 x 2 1344: 14T35 2688: 14T44 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7:C_3$
Low degree siblings
42T2494, 42T2495 x 2, 42T2496 x 2, 42T2497, 42T2498, 42T2510Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 183 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. |