Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $156$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,16,7,14,17,4,12,20,2,10,18,3,9,15)(5,11,19)(6,8,21), (1,11,4,8)(2,9,6,10)(3,13)(5,14)(7,12)(16,17,20,21,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
42T7460, 45T7533 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 255 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $96018048000=2^{10} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |