Group action invariants
| Degree $n$: | $45$ | |
| Transitive number $t$: | $39$ | |
| Group: | $C_5\times C_3^2:S_3$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $15$ | |
| Generators: | (1,41,21,13,38,32,11,5,28,23,2,40,19,15,37,31,12,4,29,24,3,42,20,14,39,33,10,6,30,22)(7,17,26,34,45,9,18,27,35,43,8,16,25,36,44), (4,5,6)(7,8,9)(13,14,15)(16,18,17)(22,24,23)(25,27,26)(31,32,33)(34,36,35)(40,41,42)(43,45,44), (1,2,3)(4,34,5,35,6,36)(7,24,9,23,8,22)(10,11,12)(13,45,14,43,15,44)(16,31,17,32,18,33)(19,20,21)(25,41,26,42,27,40)(28,29,30)(37,39,38) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $6$: $S_3$ x 4 $10$: $C_{10}$ $18$: $C_3^2:C_2$ $54$: $(C_3^2:C_3):C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $S_3$
Degree 5: $C_5$
Degree 9: $(C_3^2:C_3):C_2$
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, 17] |
| Character table: not available. |