Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $20$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,18,19,9,14,2,8,5,16)(3,17,10,4,7,15,11,13,12)(20,25,34,35,33,37,29,26,32)(21,23,38,27,30,24,36,31,22), (1,25,5,32,9,20,13,27,17,34,2,22,6,29,10,36,14,24,18,31,3,38,7,26,11,33,15,21,19,28,4,35,8,23,12,30,16,37) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $18$: $D_{9}$ 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 53 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. |