Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $35$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,2,38,13,35)(3,36,5,32,8,26)(4,34,16,29,15,31)(6,30,19,23,10,22)(7,28,11,20,17,27)(9,24,14,33,12,37)(18,25), (1,32,9,27,16,25,15,28,7,33,19,35)(2,29,17,22,4,23,14,31,18,38,12,37)(3,26,6,36,11,21,13,34,10,24,5,20)(8,30) | |
| $|\Aut(F/K)|$: | $1$ |
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 8: $D_{4}$ 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$ 72: 12T42 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 54 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |