Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $151$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,3,6)(2,4)(10,15,12,13)(11,14)(16,18)(19,21,20), (1,21,16)(2,19,17)(3,20,18)(4,15,5,13,6,14)(7,10)(8,11,9,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 2520: $A_7$ 5040: $A_7\times C_2$ 161280: 14T53 322560: 14T56 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $A_7$
Low degree siblings
42T4982, 42T4983, 42T4984Siblings 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: | $705438720=2^{10} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |