Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $991$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11)(2,12)(3,20,7,15)(4,19,8,16)(5,14,9,17)(6,13,10,18), (1,20,8,15)(2,19,7,16)(3,14)(4,13)(5,11,10,17,6,12,9,18), (1,19,18,2,20,17)(3,4)(7,12,9,8,11,10)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 120: $S_5$ 240: $S_5\times C_2$ 1920: $(C_2^4:A_5) : C_2$ x 3 3840: $C_2 \wr S_5$ x 3 30720: 20T555 61440: 20T664 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $(C_2^4:A_5) : C_2$
Low degree siblings
20T989 x 4, 20T991 x 3, 40T153072 x 2, 40T153179 x 2, 40T153265 x 2, 40T153389 x 2, 40T153405 x 2, 40T153407 x 2, 40T153530 x 2, 40T153532 x 2, 40T153701 x 2, 40T153708 x 2, 40T153711 x 4, 40T153805 x 2, 40T153809 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 265 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1966080=2^{17} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |