Group action invariants
| Degree $n$: | $40$ | |
| Transitive number $t$: | $20$ | |
| Group: | $C_{10}\times D_4$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $20$ | |
| Generators: | (1,34,27,20,10,3,36,26,18,11,2,33,28,19,9,4,35,25,17,12)(5,39,32,24,15,7,38,29,21,13,6,40,31,23,16,8,37,30,22,14), (1,21)(2,22)(3,24)(4,23)(5,28)(6,27)(7,26)(8,25)(9,32)(10,31)(11,29)(12,30)(13,33)(14,34)(15,35)(16,36)(17,38)(18,37)(19,40)(20,39), (1,35,28,18,10)(2,36,27,17,9)(3,33,25,20,11,4,34,26,19,12)(5,37,31,21,15)(6,38,32,22,16)(7,40,30,24,13,8,39,29,23,14) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $5$: $C_5$ $8$: $D_{4}$ x 2, $C_2^3$ $10$: $C_{10}$ x 7 $16$: $D_4\times C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$, $D_{4}$ x 2
Degree 5: $C_5$
Degree 8: $D_4\times C_2$
Degree 10: $C_{10}$ x 3
Low degree siblings
There are no siblings with degree $\leq 10$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 50 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $80=2^{4} \cdot 5$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [80, 46] |
| Character table: not available. |