Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $47$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,24,9,23,19,36,3,38,2,31,15,27,17,22,10,30,6,21)(4,26,8,35,13,32,5,33,14,20,11,37,12,25,18,29,16,34)(7,28), (1,37,14,28)(2,29,13,36)(3,21,12,25)(4,32,11,33)(5,24,10,22)(6,35,9,30)(7,27,8,38)(15,20,19,26)(16,31,18,34)(17,23) | |
| $|\Aut(F/K)|$: | $1$ |
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: $D_{4}$ 9: $C_9$ 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$, $D_{18}$, 36T2 54: $C_9\times S_3$, 18T19 72: 12T42, 36T15, 36T24 108: 36T63, 36T69 162: 18T74 216: 36T181, 36T189 324: 36T461 648: 36T966 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 209 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $233928=2^{3} \cdot 3^{4} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |