Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $16$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,16,15,7,19)(2,17,4,14,18,12)(3,6,11,13,10,5)(20,31,30,37,26,27)(21,24,22,36,33,35)(23,29,25,34,28,32), (1,27,12,33,4,20,15,26,7,32,18,38,10,25,2,31,13,37,5,24,16,30,8,36,19,23,11,29,3,35,14,22,6,28,17,34,9,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 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: | $4332=2^{2} \cdot 3 \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |