Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $132$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,18,8,21)(2,12,16,7,20)(3,10,17,9,19)(13,14,15), (1,14,19,8,16,4,11,2,13,21,7,17,6,12,3,15,20,9,18,5,10) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 2520: $A_7$ 7560: 21T44 1837080: 21T121 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $A_7$
Low degree siblings
21T132Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 246 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5511240=2^{3} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |