Group action invariants
| Degree $n$: | $11$ | |
| Transitive number $t$: | $8$ | |
| Group: | $S_{11}$ | |
| CHM label: | $S11$ | |
| Parity: | $-1$ | |
| Primitive: | yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $\card{\Aut(F/K)}$: | $1$ | |
| Generators: | (1,2), (1,2,3,4,5,6,7,8,9,10,11) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Prime degree - none
Low degree siblings
22T45Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| Label: | not available |
| Character table: not available. |