Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $462$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,12,17)(2,9,11,16)(3,10,15,20)(4,6,14,19)(5,7,13,18), (1,2,3,4,5)(11,18,14,16,12,19,15,17,13,20) | |
| $|\Aut(F/K)|$: | $5$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 6: $S_3$ 10: $C_{10}$ 24: $S_4$ 30: $S_3 \times C_5$ 120: 20T34 3000: 15T51 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 5: None
Degree 10: None
Low degree siblings
20T462 x 3, 30T875 x 2, 40T10520 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 190 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $15000=2^{3} \cdot 3 \cdot 5^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |