Group action invariants
| Degree $n$ : | $15$ | |
| Transitive number $t$ : | $97$ | |
| CHM label : | $[A(5)^{3}:2]S(3)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,6)(9,12), (1,11)(2,7)(4,14)(5,10)(8,13), (1,4)(6,9)(11,14), (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: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 5: None
Low degree siblings
18T946, 30T2327, 30T2331, 30T2332, 30T2333, 36T46223, 36T46224, 36T46225, 45T2114Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 70 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. |