Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $344$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,9,4,17,12,5,19,14,7,2,15,10,3,18,11,6,20,13,8), (1,2)(11,12)(13,14)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 5: $C_5$ 10: $C_{10}$ 20: 20T1 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ 320: 20T75 2560: 20T256 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_{10}$
Low degree siblings
20T333 x 24, 20T344 x 23, 40T3051 x 24, 40T3956 x 48, 40T4002 x 48, 40T4321 x 48, 40T4511 x 24, 40T4518 x 48, 40T4520 x 48, 40T4526 x 48, 40T4533 x 24, 40T4695 x 24, 40T4812 x 24, 40T4813 x 48, 40T4814 x 96, 40T4815 x 96, 40T4816 x 96, 40T5057 x 24, 40T5060 x 24, 40T5061 x 48, 40T5064 x 48, 40T5066 x 48, 40T5067 x 48, 40T5070 x 48, 40T5071 x 96, 40T5074 x 96, 40T5075 x 96, 40T5078 x 96, 40T5079 x 96, 40T5082 x 96, 40T5083 x 96, 40T5085 x 96, 40T5088 x 96, 40T5090 x 96, 40T5091 x 96, 40T5093 x 96, 40T5096 x 96, 40T5097 x 96, 40T5100 x 96, 40T5101 x 96, 40T5104 x 96, 40T5105 x 96, 40T5108 x 96, 40T5109 x 96, 40T5112 x 96, 40T5113 x 96, 40T5115 x 96, 40T5118 x 96, 40T5120 x 96Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 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. |