Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $10$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $19$ | |
| Generators: | (1,18,16,14,12,10,8,6,4,2,19,17,15,13,11,9,7,5,3)(20,23,26,29,32,35,38,22,25,28,31,34,37,21,24,27,30,33,36), (1,25,18,33,16,22,14,30,12,38,10,27,8,35,6,24,4,32,2,21,19,29,17,37,15,26,13,34,11,23,9,31,7,20,5,28,3,36) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19$: $C_{19}$ $38$: $D_{19}$, $C_{38}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T10 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 209 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $722=2 \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [722, 3] |
| Character table: not available. |