Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $14$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,10)(20,27,34,22,29,36,24,31,38,26,33,21,28,35,23,30,37,25,32), (1,21,15,30,17,34)(2,23,7,33,5,29)(3,25,18,36,12,24)(4,27,10,20,19,38)(6,31,13,26,14,28)(8,35,16,32,9,37)(11,22) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $C_6$ $57$: $C_{19}:C_{3}$ $114$: $C_{19}:C_{6}$, 38T4 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T14 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 75 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2166=2 \cdot 3 \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |