Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $46$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,15,13,4,11,14,18,17,3,16,8,10,19,12,9,5,6)(21,28,27,38,31,32)(22,36,34,37,23,25)(24,33,29,35,26,30), (1,27,9,34,19,38,3,24,2,35,15,25,17,22,10,23,6,29)(4,32,8,26,13,28,5,21,14,36,11,31,12,20,18,30,16,33)(7,37) | |
| $|\Aut(F/K)|$: | $1$ |
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 9: $C_9$ 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3 36: $C_6\times S_3$, $D_{18}$, 36T2 54: $C_9\times S_3$, 18T19 108: 36T63, 36T69 162: 18T74 324: 36T461 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 121 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $116964=2^{2} \cdot 3^{4} \cdot 19^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |