Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $140$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (4,17,10,9,20,5,16,12,8,19,6,18,11,7,21), (1,16,4,2,18,6)(3,17,5)(7,12,14,9,10,13)(8,11,15)(19,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 2520: $A_7$ 5040: $A_7\times C_2$ 15120: 21T57 3674160: 21T128 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $A_7$
Low degree siblings
21T140, 42T2643 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 150 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $11022480=2^{4} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |