Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $139$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $3$ | |
| 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) |
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: | not available |
| Character table: not available. |