Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $90$ | |
| CHM label : | $[S(3)^{5}]A(5)=S(3)wrA(5)$ | |
| 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), (5,10), (1,13)(2,14)(3,6)(4,7)(8,11)(9,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 60: $A_5$ 120: $A_5\times C_2$ 960: $C_2^4 : A_5$ 1920: $C_2 \wr A_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $A_5$
Low degree siblings
30T1811, 30T1820, 30T1823, 30T1827, 45T1509Siblings 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: | $466560=2^{7} \cdot 3^{6} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |