Group action invariants
| Degree $n$: | $45$ | |
| Transitive number $t$: | $12$ | |
| Group: | $C_5\times C_9:C_3$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $15$ | |
| Generators: | (1,8,13,20,26,31,38,45,6,10,18,23,30,35,40,2,9,15,19,25,33,39,44,5,12,16,22,29,34,42,3,7,14,21,27,32,37,43,4,11,17,24,28,36,41), (1,20,38,10,30,2,19,39,12,29,3,21,37,11,28)(4,23,42,13,33)(5,24,40,14,31)(6,22,41,15,32)(7,25,45,17,34,9,26,43,16,35,8,27,44,18,36) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ x 4 $5$: $C_5$ $9$: $C_3^2$ $27$: $C_9:C_3$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $C_3$
Degree 5: $C_5$
Degree 9: $C_9:C_3$
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 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $135=3^{3} \cdot 5$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [135, 4] |
| Character table: not available. |