Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1036$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,5,20,17,15,13,8,10,12,2,4,6,19,18,16,14,7,9,11), (1,17,13,9)(2,18,14,10)(3,11,19,16,4,12,20,15), (1,18,14,9,2,17,13,10)(3,11,8,19)(4,12,7,20)(5,6) | |
| $|\Aut(F/K)|$: | $2$ |
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: $D_4\times C_2$ 14400: $(A_5^2 : C_2):C_2$ 28800: 20T548 57600: 20T658 3686400: 20T1009 7372800: 20T1028 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $(A_5^2 : C_2):C_2$
Low degree siblings
20T1036 x 3, 40T178058 x 2, 40T178067 x 4, 40T178068 x 4, 40T178132 x 2, 40T178134 x 2, 40T178151 x 4, 40T178152 x 4, 40T178153 x 4, 40T178154 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 396 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. |