Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $25$ | |
| Group : | $C_5\times C_5^2:C_3$ | |
| CHM label : | $[5^{3}]3=5wr3$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15), (3,6,9,12,15) | |
| $|\Aut(F/K)|$: | $5$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 5: $C_5$ 15: $C_{15}$ 75: $C_5^2 : C_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 5: None
Low degree siblings
15T25 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $375=3 \cdot 5^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [375, 6] |
| Character table: Data not available. |