Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $83$ | |
| CHM label : | $[3^{5}:2]S(5)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11)(2,7)(4,14)(5,10)(8,13), (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15), (1,4)(6,9)(11,14) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 120: $S_5$ 240: $S_5\times C_2$ 720: $S_5 \times S_3$ 19440: 15T70 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $S_5$
Low degree siblings
15T83, 30T1237 x 2, 30T1243 x 2, 30T1244 x 2, 30T1246 x 2, 30T1254 x 2, 45T867 x 2, 45T880Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 72 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $58320=2^{4} \cdot 3^{6} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |