Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $15$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,7,10,13,16,19,3,6,9,12,15,18,2,5,8,11,14,17)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,38)(35,37), (1,20,19,24)(2,35,18,28)(3,31,17,32)(4,27,16,36)(5,23,15,21)(6,38,14,25)(7,34,13,29)(8,30,12,33)(9,26,11,37)(10,22) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2888=2^{3} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |