Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $340$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,18,6,14,2,9,17,5,13)(3,12,20,7,15,4,11,19,8,16), (1,3,6,7,10,12,14,16,18,19)(2,4,5,8,9,11,13,15,17,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 10: $C_{10}$ x 3 20: 20T3 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ x 3 320: 20T72 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
20T329 x 24, 20T340 x 23, 40T3058 x 24, 40T3245 x 48, 40T3322 x 24, 40T3405 x 12, 40T3529 x 192, 40T4007 x 48, 40T4064 x 96, 40T4291 x 24, 40T4394 x 48, 40T4510 x 24, 40T4519 x 48, 40T4524 x 48, 40T4525 x 48, 40T4535 x 24, 40T4578 x 48, 40T4691 x 12, 40T4953 x 24, 40T4954 x 48, 40T4957 x 96, 40T4958 x 96, 40T4959 x 96, 40T5058 x 24, 40T5059 x 24, 40T5062 x 48, 40T5063 x 48, 40T5065 x 48, 40T5068 x 48, 40T5069 x 48, 40T5072 x 96, 40T5073 x 96, 40T5076 x 96, 40T5077 x 96, 40T5080 x 96, 40T5081 x 96, 40T5084 x 96, 40T5086 x 96, 40T5087 x 96, 40T5089 x 96, 40T5092 x 96, 40T5094 x 96, 40T5095 x 96, 40T5098 x 96, 40T5099 x 96, 40T5102 x 96, 40T5103 x 96, 40T5106 x 96, 40T5107 x 96, 40T5110 x 96, 40T5111 x 96, 40T5114 x 96, 40T5116 x 96, 40T5117 x 96, 40T5119 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. |