Group action invariants
| Degree $n$ : | $45$ | |
| Transitive number $t$ : | $144$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,22,10,5)(2,24,12,6)(3,23,11,4)(7,26,34,17)(8,27,36,16)(9,25,35,18)(13,28)(14,30)(15,29)(19,31,37,41)(20,32,39,40)(21,33,38,42)(43,44), (1,42,44,20,32,26,29,5,16,10,15,36,3,40,45,21,31,27,30,6,18,11,13,34,2,41,43,19,33,25,28,4,17,12,14,35)(7,38,22,9,37,24,8,39,23) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_4$ x 2, $C_2^2$ 6: $S_3$, $C_6$ x 3 8: $C_4\times C_2$ 12: $D_{6}$ 18: $S_3\times C_3$ 20: $F_5$ 40: $F_{5}\times C_2$ 54: $(C_9:C_3):C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $S_3$
Degree 5: $F_5$
Degree 9: $(C_9:C_3):C_2$
Degree 15: $F_5 \times S_3$
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: | $1080=2^{3} \cdot 3^{3} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1080, 271] |
| Character table: Data not available. |