Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $49$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,32,24,16,8,38,29,22,14,6,35,28,20,12,3,34,26,17,10,2,31,23,15,7,37,30,21,13,5,36,27,19,11,4,33,25,18,9), (1,17,34,11,28,5,22,37,15,31,10,25,3,19,36,14,30,8,23,2,18,33,12,27,6,21,38,16,32,9,26,4,20,35,13,29,7,24) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19$: $C_{19}$ $38$: $C_{38}$ $4980736$: 38T48 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: $C_{19}$
Low degree siblings
38T49 x 13796Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 27,632 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $9961472=2^{19} \cdot 19$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |