Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $75$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,19,9,18,4,13,2,12,20,8,16,6,15,3,11,21,7,17,5,14), (2,3)(4,19)(5,20)(6,21)(7,17)(8,18)(9,16)(10,13,12,14,11,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 14: $D_{7}$ 42: $D_{21}$ 10206: 21T51 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
21T75 x 25, 42T852 x 26, 42T861 x 13, 42T863 x 26Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 207 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $30618=2 \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |