Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $21$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,13,6,18,11,4,16,9,2,14,7,19,12,5,17,10,3,15,8)(20,36,34)(21,24,26)(22,31,37)(23,38,29)(25,33,32)(27,28,35), (1,20,19,22,12,36)(2,37,7,27,4,33)(3,35,14,32,15,30)(5,31,9,23,18,24)(6,29,16,28,10,21)(8,25,11,38,13,34)(17,26) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $S_3$, $C_6$ $18$: $S_3\times C_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 54 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6498=2 \cdot 3^{2} \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |