Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $50$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,30,2,29)(3,28,4,27)(5,25,6,26)(7,23)(8,24)(9,21,10,22)(11,20)(12,19)(13,18,14,17)(15,16)(31,38)(32,37)(33,35)(34,36), (1,37,2,38)(3,36)(4,35)(5,33)(6,34)(7,32,8,31)(9,29,10,30)(11,28,12,27)(13,26)(14,25)(15,23,16,24)(17,21,18,22) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $38$: $D_{19}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: $D_{19}$
Low degree siblings
38T50 x 510, 38T51 x 511Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 7,676 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. |