Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $39$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,12,13,17,14,2,11,9)(3,15,6,8,16,10,5,4,19)(20,35,37,36,27,22,34,28,31)(21,25,23,24,33,38,26,32,29), (1,24,7,20,2,36,3,29,18,38,15,21,8,32,17,26,19,31,11,30,5,34,10,37,9,25,13,35,16,33,4,22,14,28,12,23)(6,27) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 4: $C_4$ 6: $S_3$, $C_6$ 9: $C_9$ 12: $C_{12}$, $C_3 : C_4$ 18: $S_3\times C_3$, $C_{18}$ 36: $C_3\times (C_3 : C_4)$, $C_{36}$ 54: $C_9\times S_3$ 108: 36T62 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 60 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: | Data not available |
| Character table: Data not available. |