Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $749$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,17,16,13)(2,19,18,15,14)(3,12,10,8,5,4,11,9,7,6), (1,4,16,7,9)(2,3,15,8,10)(5,18,20,11,13)(6,17,19,12,14), (1,14,6,18,9)(2,13,5,17,10)(3,15,7,19,12,4,16,8,20,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 10: $C_{10}$ 80: $C_2^4 : C_5$ x 17 160: $C_2 \times (C_2^4 : C_5)$ x 17 1280: 20T190 2560: 20T263, 2560T? x 2 5120: 5120T? 40960: 40960T? Resolvents shown for degrees $\leq 23$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2^4 : C_5$
Low degree siblings
20T749 x 127, 20T751 x 128Siblings are shown with degree $\leq 23$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 332 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $81920=2^{14} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |