Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $43$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,15,29)(2,22,14,27)(3,24,13,25)(4,26,12,23)(5,28,11,21)(6,30,10,38)(7,32,9,36)(8,34)(16,31,19,37)(17,33,18,35), (1,11,16,9,15,18,10,6,4,3,12,7,14,8,5,13,17,19)(20,38,22,32,21,35,31,24,26)(23,29,30,27,36,28,33,37,25) | |
| $|\Aut(F/K)|$: | $1$ |
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: $S_3\times C_3$, $D_{9}$ 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$, $D_{18}$ 54: 18T19 72: 12T42, 36T24 108: 36T69 216: 36T189 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 75 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $77976=2^{3} \cdot 3^{3} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |