Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $146$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18)(2,17,3,19)(4,20,7,21)(5,16)(6,15)(8,12,11,10)(13,14), (1,6,2)(4,5,7)(8,15,14,16,11,17)(9,21,10,18,12,19)(13,20) | |
| $|\Aut(F/K)|$: | $1$ |
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
21T146, 24T24314, 42T3078 x 2, 42T3079 x 2, 42T3080 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy Classes
There are 98 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $28449792=2^{10} \cdot 3^{4} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |