Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $313$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,4,16,2,13,3,15)(5,18)(6,17)(7,19)(8,20)(9,12,10,11), (1,4,2,3)(5,16,7,13,6,15,8,14)(9,17,10,18)(11,19,12,20) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 10: $D_{5}$ 20: $D_{10}$ 160: $(C_2^4 : C_5) : C_2$ 320: $C_2\times (C_2^4 : D_5)$ 2560: 20T244 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $(C_2^4 : C_5) : C_2$
Low degree siblings
20T313 x 11, 20T319 x 6, 20T327 x 6, 40T3458 x 24, 40T3492 x 6, 40T3495 x 3, 40T3497 x 6, 40T4367 x 6, 40T4371 x 6, 40T4381 x 6, 40T4540 x 6, 40T4545 x 3, 40T4546 x 6, 40T4548 x 6, 40T4725 x 12, 40T4751 x 12, 40T4752 x 12, 40T4761 x 12, 40T4821 x 12, 40T4923 x 12, 40T4926 x 12, 40T4930 x 12, 40T4985 x 12, 40T4998 x 12, 40T5006 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5120=2^{10} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |