Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $120$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,8,10,15,17,21,2,4,9,12,14,16,19,3,5,7,11,13,18,20), (1,2,3)(5,6)(10,12)(14,15)(16,18,17)(20,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 7: $C_7$ 56: $C_2^3:C_7$ x 2 448: 14T21 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
42T1894 x 6, 42T1895 x 3, 42T1896 x 3, 42T1897 x 6, 42T1898 x 6, 42T1899 x 6, 42T1900 x 6, 42T1901 x 6, 42T1902 x 6, 42T1903 x 6, 42T1904 x 6, 42T1905 x 2, 42T1906, 42T1907 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 177 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $979776=2^{6} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |