Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $158$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,12,7,16,8,4,19,11,5,15,9,6,20,13,2,18,14,3,21,10), (1,11,15)(2,14,21,3,9,20,7,8,18,5,12,19,4,13,17)(6,10,16) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 12: $A_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
42T7693 x 2, 42T7694Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 587 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $192036096000=2^{11} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |