Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $81$ | |
| CHM label : | $[S(3)^{5}]5=S(3)wr5$ | |
| 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) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 10: $C_{10}$ 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: $C_5$
Low degree siblings
30T1117, 30T1120, 30T1121 x 4, 30T1122 x 2, 30T1123 x 4, 30T1127 x 4, 30T1128 x 4, 30T1133 x 4, 30T1146 x 2, 30T1147, 30T1149 x 2, 30T1151 x 4, 45T778 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: | $38880=2^{5} \cdot 3^{5} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |