Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $142$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (4,14,7,6,13,8)(5,15,9)(10,18,21,12,16,20,11,17,19), (1,14)(2,13)(3,15)(4,12)(5,10,6,11)(8,9)(16,19,18,21)(17,20) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 12: $C_6\times C_2$ 42: $F_7$ 84: $F_7 \times C_2$ 2688: 14T40 5376: 14T48 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $F_7$
Low degree siblings
42T2703, 42T2704, 42T2705, 42T2706, 42T2707, 42T2708, 42T2709, 42T2717Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 168 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $11757312=2^{8} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |