Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $102$ | |
| CHM label : | $[S(5)^{3}]S(3)=S(5)wrS(3)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11)(2,7)(4,14)(5,10)(8,13), (6,9), (1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15), (3,6,9,12,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ 48: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 5: None
Low degree siblings
18T958, 30T2981, 30T2984, 30T2985, 30T2986, 30T2989, 30T2990, 30T2994, 30T2998, 36T60049, 36T60050, 36T60051, 36T60052, 36T60053, 36T60054, 36T60055, 45T2638Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 140 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10368000=2^{10} \cdot 3^{4} \cdot 5^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |