Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $78$ | |
| CHM label : | $[3^{5}]S(5)=3wrS(5)$ | |
| 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), (1,4)(6,9)(11,14) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 120: $S_5$ 360: $S_5 \times C_3$ 9720: 15T63 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $S_5$
Low degree siblings
15T78, 30T1016 x 2, 30T1033 x 2, 30T1038 x 2, 45T696 x 2, 45T723Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 108 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $29160=2^{3} \cdot 3^{6} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |