Group action invariants
| Degree $n$: | $45$ | |
| Transitive number $t$: | $11$ | |
| Group: | $C_5\times He_3$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $15$ | |
| Generators: | (1,34,23,10,45,33,21,9,41,30,17,5,39,25,14)(2,36,22,12,44,32,20,7,40,29,18,4,37,27,13)(3,35,24,11,43,31,19,8,42,28,16,6,38,26,15), (1,45,40,39,34,32,30,25,22,21,17,13,10,9,4)(2,44,42,37,36,31,29,27,24,20,18,15,12,7,6)(3,43,41,38,35,33,28,26,23,19,16,14,11,8,5) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ x 4 $5$: $C_5$ $9$: $C_3^2$ $27$: $C_3^2:C_3$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $C_3$
Degree 5: $C_5$
Degree 9: $C_3^2:C_3$
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, 3] |
| Character table: not available. |