Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $36$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(20,25,30,35,21,26,31,36,22,27,32,37,23,28,33,38,24,29,34), (1,21)(2,29,11,25,6,23,13,22,7,31,4,26,12,33,16,27,18,24,19,32,10,36,15,38,8,20,14,30,17,35,9,28,5,34,3,37) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 8: $D_{4}$ 9: $C_9$ 12: $C_6\times C_2$ 18: $C_{18}$ x 3 24: $D_4 \times C_3$ 36: 36T2 72: 36T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T36Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 53 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |