Group action invariants
| Degree $n$: | $30$ | |
| Transitive number $t$: | $39$ | |
| Group: | $C_{15}\times D_5$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $15$ | |
| Generators: | (1,23,13,5,25,16,8,30,20,12,3,22,15,4,27,18,7,29,19,11,2,24,14,6,26,17,9,28,21,10), (1,15,26,8,19)(2,13,27,9,20)(3,14,25,7,21)(4,23,11,30,17)(5,24,12,28,18)(6,22,10,29,16) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $5$: $C_5$ $6$: $C_6$ $10$: $D_{5}$, $C_{10}$ $15$: $C_{15}$ $30$: $D_5\times C_3$, $C_{30}$ $50$: $D_5\times C_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: $C_3$
Degree 5: None
Degree 6: $C_6$
Degree 10: $D_5\times C_5$
Degree 15: None
Low degree siblings
30T39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $150=2 \cdot 3 \cdot 5^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [150, 8] |
| Character table: not available. |