Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $87$ | |
| CHM label : | $[S(3)^{5}]F(5)=S(3)wrF(5)$ | |
| 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), (5,10), (1,7,4,13)(2,14,8,11)(3,6,12,9) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 20: $F_5$ 40: $F_{5}\times C_2$ 320: $(C_2^4 : C_5):C_4$ 640: $((C_2^4 : C_5):C_4)\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $F_5$
Low degree siblings
30T1538, 30T1540, 30T1549, 30T1550, 30T1557, 30T1558, 30T1559Siblings 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: | $155520=2^{7} \cdot 3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |