Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $36$ | |
| CHM label : | $[3^{5}]5=3wr5$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 5: $C_5$ 15: $C_{15}$ 405: 15T26 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $C_5$
Low degree siblings
15T36 x 15, 45T164 x 8, 45T165 x 16, 45T166 x 32, 45T167 x 32, 45T168 x 64, 45T169 x 64Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 63 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1215=3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1215, 69] |
| Character table: Data not available. |