Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $12$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,12)(2,11)(3,10)(4,9)(5,8)(6,7)(13,19)(14,18)(15,17)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,38)(35,37), (1,25,4,32)(2,21,3,36)(5,28,19,29)(6,24,18,33)(7,20,17,37)(8,35,16,22)(9,31,15,26)(10,27,14,30)(11,23,13,34)(12,38) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T12 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 94 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, 8] |
| Character table: not available. |