Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $82$ | |
| CHM label : | $[F(5)^{3}]S(3)=F(5)wrS(3)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,6,12,9), (1,11)(2,7)(4,14)(5,10)(8,13), (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: $C_4$ x 2, $C_2^2$ 6: $S_3$ 8: $C_4\times C_2$ 12: $D_{6}$ 24: $S_4$, $S_3 \times C_4$ 48: $S_4\times C_2$ 96: 12T53, 12T62 192: 12T95 384: 12T150 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 5: None
Low degree siblings
30T1205, 30T1206, 30T1212, 30T1215, 30T1218, 30T1219, 30T1220Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $48000=2^{7} \cdot 3 \cdot 5^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |