Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $101$ | |
| CHM label : | $[S(5)^{3}]3=S(5)wr3$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (6,9), (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: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 5: None
Low degree siblings
18T953, 30T2611, 30T2615, 30T2621 x 2, 30T2630 x 2, 30T2632, 30T2634, 36T53410 x 2, 36T53411, 36T53412 x 2, 36T53413, 36T53414, 45T2365Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 133 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5184000=2^{9} \cdot 3^{4} \cdot 5^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |