Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $53$ | |
| Group : | $C_5\times C_5:D_4$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,9,20,7,17,5,15,4,14,2,12,10,19,8,18,6,16,3,13), (1,12)(2,11)(3,14)(4,13)(5,16)(6,15)(7,18)(8,17)(9,19)(10,20) | |
| $|\Aut(F/K)|$: | $10$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: $D_5\times C_5$
Low degree siblings
20T53 x 3, 40T152 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $200=2^{3} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [200, 31] |
| Character table: Data not available. |