Group action invariants
| Degree $n$ : | $45$ | |
| Transitive number $t$ : | $37$ | |
| Group : | $C_5\times He_3:C_2$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,44,12,7,21,16,30,26,38,36,3,43,11,8,20,18,29,25,39,35,2,45,10,9,19,17,28,27,37,34)(4,31,14,40,24,5,33,15,42,23)(6,32,13,41,22), (1,3)(4,36)(5,35)(6,34)(7,24)(8,23)(9,22)(10,11)(13,43)(14,45)(15,44)(16,32)(17,31)(18,33)(19,21)(25,41)(26,40)(27,42)(29,30)(37,39) | |
| $|\Aut(F/K)|$: | $5$ |
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: $C_3^2 : C_6$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 3: $S_3$
Degree 5: $C_5$
Degree 9: $C_3^2 : C_6$
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, 10] |
| Character table: Data not available. |