Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1015$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,15)(2,3,16)(5,12,13)(6,11,14)(7,20,17,10)(8,19,18,9), (1,12)(2,11)(3,14)(4,13)(5,16)(6,15)(7,19,8,20)(9,18)(10,17), (1,8,4,12,18,13,2,7,3,11,17,14)(5,15)(6,16)(9,19)(10,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 120: $S_5$ 240: $S_5\times C_2$ x 3 480: 20T117 1920: $(C_2^4:A_5) : C_2$ x 3 3840: $C_2 \wr S_5$ x 9 7680: 20T368 x 3 30720: 20T555 61440: 20T664 x 3 122880: 20T799 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $C_2 \wr S_5$
Low degree siblings
20T1015 x 15, 40T162300 x 8, 40T162378 x 8, 40T162506 x 8, 40T162681 x 8, 40T162682 x 8, 40T162685 x 8, 40T162686 x 8, 40T162820 x 8, 40T162822 x 8, 40T162888 x 8, 40T162890 x 8, 40T163186 x 8, 40T163188 x 8, 40T163195 x 8, 40T163198 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 506 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3932160=2^{18} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |