Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $44$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,19,24,14,37,8,26,16,28,18,38,9,31,2,34,5,30)(3,20,10,36,7,21,11,22,12,27,17,33,4,25,15,23,13,32)(6,35), (1,27,15,34,12,23,14,24,19,36,3,28)(2,37,8,21,4,38,13,33,7,30,11,32)(5,29,6,20,18,26,10,22,9,31,16,25)(17,35) | |
| $|\Aut(F/K)|$: | $1$ |
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: $S_3\times C_3$, $C_{18}$ x 3 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$, 36T2 54: $C_9\times S_3$ 72: 12T42, 36T15 108: 36T63 216: 36T181 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 90 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. |