Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $86$ | |
| CHM label : | $[S(3)^{5}]D(5)=S(3)wrD(5)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4)(2,8)(3,12)(6,9)(7,13)(11,14), (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15), (5,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 10: $D_{5}$ 20: $D_{10}$ 160: $(C_2^4 : C_5) : C_2$ 320: $C_2\times (C_2^4 : D_5)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $D_{5}$
Low degree siblings
30T1344, 30T1345 x 2, 30T1346, 30T1347, 30T1348 x 2, 30T1355, 30T1356, 30T1357, 30T1362 x 2, 30T1364, 30T1365 x 2, 30T1367 x 2, 45T935 x 2Siblings 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: | $77760=2^{6} \cdot 3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |