Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $42$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,30,14,29,16,23,9,25,5,37,19,33,8,28,18,36,2,27)(3,24,7,31,12,35,4,21,13,32,10,22,11,38,17,20,15,26)(6,34), (1,27,11,23,4,22,7,36,3,30,2,38,16,21,10,31,18,24)(5,33,12,34,9,20,13,26,14,37,19,35,6,25,17,32,15,29)(8,28) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $S_3$, $C_6$ $9$: $C_9$ $18$: $S_3\times C_3$, $D_{9}$, $C_{18}$ $54$: $C_9\times S_3$, 18T19 $162$: 18T74 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 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $58482=2 \cdot 3^{4} \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |