Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,9,21,17,22,6,23,14,24,3,25,11,26,19,27,8,28,16,29,5,30,13,31,2,32,10,33,18,34,7,35,15,36,4,37,12,38), (1,22,16,25,10,20)(2,26,8,31,17,29)(3,30,19,37,5,38)(4,34,11,24,12,28)(6,23,14,36,7,27)(9,35)(13,32,15,21,18,33) | |
| $|\Aut(F/K)|$: | $1$ |
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 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$, $D_{9}$ 36: $C_6\times S_3$, $D_{18}$ 54: 18T19 108: 36T69 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 51 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. |