Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1040$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,2,12)(3,14)(4,13)(5,8,6,7)(9,19,17,16)(10,20,18,15), (1,14,17,10,5)(2,13,18,9,6)(3,4)(7,20,15,12,8,19,16,11), (1,14,10,5)(2,13,9,6)(3,12,8,15,4,11,7,16)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
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 2, $C_2^3$ 16: $D_4\times C_2$ 28800: $S_5^2 \wr C_2$ 57600: 20T655 7372800: 20T1022 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $S_5^2 \wr C_2$
Low degree siblings
20T1038 x 2, 20T1040, 40T178078 x 2, 40T178080 x 2, 40T178082 x 2, 40T178083 x 2, 40T178085 x 2, 40T178093 x 2, 40T178103, 40T178105, 40T178139 x 2, 40T178140 x 2, 40T178141 x 2, 40T178142 x 2, 40T178143 x 2, 40T178144 x 2, 40T178145 x 2, 40T178146 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 378 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $14745600=2^{16} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |