Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $955$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,18,7,2,4,17,8)(5,19,13,12,6,20,14,11)(9,15)(10,16), (1,2)(3,19,7,11)(4,20,8,12)(9,10)(13,14)(15,16)(17,18), (1,16,18,12,5,20,9,4)(2,15,17,11,6,19,10,3)(7,13)(8,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 4, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 2, $C_4\times C_2^2$ 32: $C_4\wr C_2$ x 4, $C_2^2 \wr C_2$, $C_4 \times D_4$ x 2, $C_2 \times (C_2^2:C_4)$, 16T34 x 2, 16T37 64: 16T111 x 2, 32T239 128: 16T211 800: $F_5 \wr C_2$ 1600: 20T212 3200: 20T271 204800: 20T860 409600: 20T923 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $F_5 \wr C_2$
Low degree siblings
20T955 x 7, 40T147042 x 4, 40T147045 x 4, 40T147092 x 4, 40T147095 x 4, 40T147142 x 4, 40T147145 x 4, 40T147148 x 4, 40T147149 x 4, 40T147197 x 8, 40T147234 x 4, 40T147235 x 4, 40T147236 x 8, 40T147237 x 8, 40T147238 x 8, 40T147239 x 8, 40T147240 x 8, 40T147241 x 8, 40T147242 x 8, 40T147243 x 8, 40T147245 x 4, 40T147254 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 275 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $819200=2^{15} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |