Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $31$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,17,2,16,3,15,4,14,5,13,6,12,7,22,8,21,9,20,10,19,11,18), (1,6,4,7,8)(2,10,9,5,11)(12,21,17,20,15,16,18,22,19,13) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $8$: $D_{4}$ $10$: $D_{5}$, $C_{10}$ x 3 $20$: $D_{10}$, 20T3 $40$: 20T7, 20T12 $50$: $D_5\times C_5$ $100$: 20T24 $200$: 20T53 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T218, 44T219, 44T220Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $24200=2^{3} \cdot 5^{2} \cdot 11^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |