Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1039$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,20,7,16,4,19,8,15)(5,18,13,6,17,14)(9,10)(11,12), (1,16,5,4,14,12)(2,15,6,3,13,11)(7,10,20,18,8,9,19,17) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $D_{4}$ x 2, $C_4\times C_2$ 16: $C_2^2:C_4$ 28800: $S_5^2 \wr C_2$ 57600: 20T654 7372800: 20T1022 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
20T1039, 20T1041 x 2, 40T178077 x 2, 40T178079 x 2, 40T178081 x 2, 40T178084 x 2, 40T178086 x 2, 40T178094 x 2, 40T178104, 40T178106, 40T178135 x 2, 40T178136 x 2, 40T178137 x 2, 40T178138 x 2, 40T178147 x 2, 40T178148 x 2, 40T178149 x 2, 40T178150 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 378 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. |