Group action invariants
| Degree $n$ : | $45$ | |
| Transitive number $t$ : | $38$ | |
| Group : | $C_5\times D_9:C_3$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,25,21,45,38,17,11,34,29,7,2,26,19,43,37,18,12,35,30,9,3,27,20,44,39,16,10,36,28,8)(4,15,24,31,42,5,14,23,33,40)(6,13,22,32,41), (1,38,30,20,11,2,39,28,19,12)(3,37,29,21,10)(4,25,31,7,13,35,42,16,23,45,6,26,33,9,15,36,41,17,24,43,5,27,32,8,14,34,40,18,22,44) | |
| $|\Aut(F/K)|$: | $5$ |
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: $(C_9:C_3):C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $S_3$
Degree 5: $C_5$
Degree 9: $(C_9:C_3):C_2$
Degree 15: $S_3 \times C_5$
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, 11] |
| Character table: Data not available. |