Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $159$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,4,2)(3,7)(8,14)(9,10,11,12)(15,20,19,21,18,17), (1,15,8,3,19,14,7,16,13,4,21,10,6,17,12,2,18,11)(5,20,9) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
42T7892 x 2, 42T7893, 42T7894 x 2, 42T7895, 42T7896Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 1,165 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $384072192000=2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |