Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $56$ | |
| CHM label : | $[3^{5}]F(5)=3wrF(5)$ | |
| 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), (1,7,4,13)(2,14,8,11)(3,6,12,9) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 4: $C_4$ 6: $C_6$ 12: $C_{12}$ 20: $F_5$ 60: $F_5\times C_3$ 1620: 15T41 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $F_5$
Low degree siblings
15T56, 30T551 x 2, 30T552 x 2, 30T555, 45T372, 45T373, 45T377 x 2Siblings 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: | $4860=2^{2} \cdot 3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |