Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $876$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11)(2,12)(3,10)(4,9)(5,8)(6,7)(13,20)(14,19)(15,18,16,17), (1,11,6,8,9,3,13,20,17,15)(2,12,5,7,10,4,14,19,18,16), (1,12)(2,11)(3,13,20,10)(4,14,19,9)(5,8,18,15)(6,7,17,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 3 32: $C_2^2 \wr C_2$ 200: $D_5^2 : C_2$ 400: 20T92 800: 20T168 51200: 20T637 102400: 20T756 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $D_5^2 : C_2$
Low degree siblings
20T876 x 23, 40T105779 x 12, 40T105792 x 12, 40T105834 x 12, 40T105879 x 24, 40T106002 x 12, 40T106003 x 12, 40T106148 x 24, 40T106149 x 24, 40T106150 x 24, 40T106151 x 24, 40T106152 x 24, 40T106153 x 24, 40T106154 x 24, 40T106155 x 24, 40T106163 x 24, 40T106164 x 24, 40T106165 x 24, 40T106171 x 24, 40T106182 x 24, 40T106190 x 48, 40T106193 x 24, 40T106195 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 230 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $204800=2^{13} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |