Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $40$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,16,4,6,12,11,8,18,10,5,9,2,19,13,14,17,7,15)(20,31,33,23,35,32,28,29,24,30,38,36,27,34,37,22,21,26), (1,27,16,20,15,23,10,38,4,37,12,32,14,26,5,34,17,36)(2,24)(3,21,7,28,8,25,13,29,19,30,11,35,9,22,18,33,6,31) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $3$: $C_3$ $4$: $C_2^2$ $6$: $S_3$, $C_6$ x 3 $9$: $C_9$ $12$: $D_{6}$, $C_6\times C_2$ $18$: $S_3\times C_3$, $C_{18}$ x 3 $36$: $C_6\times S_3$, 36T2 $54$: $C_9\times S_3$ $108$: 36T63 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 63 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $38988=2^{2} \cdot 3^{3} \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |