Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1022$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,6,11,10,16,3,14,7,20)(2,18,5,12,9,15,4,13,8,19), (1,12,3,13,10,16,7,20)(2,11,4,14,9,15,8,19)(5,17,6,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 28800: $S_5^2 \wr C_2$ 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
20T1026, 20T1030, 20T1031, 32T2713780, 40T171517, 40T171518, 40T171519, 40T171520, 40T171521, 40T171522, 40T171523, 40T171524, 40T171525, 40T171526, 40T171529, 40T171530, 40T171533, 40T171534Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 189 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7372800=2^{15} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |