Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $98$ | |
| CHM label : | $[1/2.S(5)^{3}]3$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4)(11,14), (3,6)(9,12), (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) 3: $C_3$ 12: $A_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 5: None
Low degree siblings
18T947, 30T2335 x 2, 30T2336, 30T2337, 36T46226, 36T46227 x 2, 45T2115Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 71 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2592000=2^{8} \cdot 3^{4} \cdot 5^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |