Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $11$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,27,10,25,19,23,9,21,18,38,8,36,17,34,7,32,16,30,6,28,15,26,5,24,14,22,4,20,13,37,3,35,12,33,2,31,11,29), (1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $38$: $D_{19}$ x 2 $76$: $D_{38}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T11 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 121 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1444=2^{2} \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [1444, 9] |
| Character table: not available. |