Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $46$ | |
| CHM label : | $[3^{5}]D(5)=3wrD(5)$ | |
| 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) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 10: $D_{5}$ 30: $D_5\times C_3$ 810: 15T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $D_{5}$
Low degree siblings
15T46 x 7, 30T388 x 4, 30T391 x 8, 45T250 x 4, 45T251 x 4, 45T261 x 8, 45T262 x 16, 45T263 x 16Siblings 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: | $2430=2 \cdot 3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |