Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $139$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,2,12,3,11)(4,17)(5,16)(6,18)(7,21,13)(8,20,14)(9,19,15), (1,4)(2,5)(3,6)(7,18,10,8,16,11,9,17,12)(19,20,21) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 5040: $S_7$ 15120: 21T56 3674160: 21T130 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
21T139, 42T2642 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 429 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $11022480=2^{4} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |