Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $299$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,13,9,5,18,11,8,4,16,14,7,3,19,12,6,2,17,15,10), (1,6,4,9,2,7,5,10,3,8)(11,18,12,19,13,20,14,16,15,17) | |
| $|\Aut(F/K)|$: | $5$ |
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: $D_5^2 : C_2$, 20T53 1000: 20T178, 20T185 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: None
Low degree siblings
20T299 x 7, 40T3014 x 8, 40T3040 x 4, 40T3041 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 230 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5000=2^{3} \cdot 5^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |