Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $153$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,3,2,6,5,4)(8,9,14)(11,12,13)(15,20,19,18,16), (1,8,17,7,12,18,3,9,16,4,11,20)(2,14,19)(5,10,15,6,13,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
45T7189 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 267 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $48009024000=2^{9} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |