Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $48$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,15,29,6,20,34,9,23,38,13,28,4,17,32,7,21,35,11,26)(2,16,30,5,19,33,10,24,37,14,27,3,18,31,8,22,36,12,25), (1,38,36,33,31,29,27,25,24,22,20,18,15,13,12,9,7,5,3)(2,37,35,34,32,30,28,26,23,21,19,17,16,14,11,10,8,6,4) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $19$: $C_{19}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: $C_{19}$
Low degree siblings
38T48 x 13796Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 13,816 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4980736=2^{18} \cdot 19$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |