Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $76$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18)(2,16)(3,17)(4,14,5,15,6,13)(7,11,9,10,8,12)(19,20,21), (1,6,7,10,13,16,19,2,5,9,12,15,17,20,3,4,8,11,14,18,21) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 14: $D_{7}$ 42: 21T3 10206: 21T51 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
21T76 x 25, 42T853 x 26, 42T862 x 26, 42T864 x 13Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 288 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. |