Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $669$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,15,18,5,4,10,14,19,7)(2,11,16,17,6,3,9,13,20,8), (1,19,8,14,2,20,7,13)(3,17,5,16,4,18,6,15)(9,10)(11,12) | |
| $|\Aut(F/K)|$: | $4$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $(C_2^4:A_5) : C_2$, $C_2 \wr S_5$ x 2
Low degree siblings
20T664 x 6, 20T669 x 5, 40T18934 x 6, 40T19059 x 12, 40T19085 x 6, 40T19086 x 6, 40T19087 x 6, 40T19107 x 6, 40T19108 x 6, 40T19114 x 12, 40T19141 x 3, 40T19195 x 6, 40T19196 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 126 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $61440=2^{12} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |