Group action invariants
| Degree $n$: | $45$ | |
| Transitive number $t$: | $30$ | |
| Group: | $C_5\times He_3:C_2$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $5$ | |
| Generators: | (1,8,14,19,27,31,39,45,6,11,16,24,30,35,41)(2,9,13,21,26,33,37,44,5,10,17,23,29,34,40)(3,7,15,20,25,32,38,43,4,12,18,22,28,36,42), (1,8,13,19,27,33,39,45,5,11,16,23,30,35,40)(2,7,15,20,26,31,37,43,4,12,17,24,29,36,42,3,9,14,21,25,32,38,44,6,10,18,22,28,34,41) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $5$: $C_5$ $6$: $S_3$, $C_6$ $10$: $C_{10}$ $18$: $S_3\times C_3$ $54$: $C_3^2 : C_6$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $C_3$
Degree 5: $C_5$
Degree 9: $C_3^2 : S_3 $
Degree 15: $C_{15}$
Low degree siblings
There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy classes
There are 50 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $270=2 \cdot 3^{3} \cdot 5$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [270, 10] |
| Character table: not available. |