Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $37$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,20,9,21,17,22,6,23,14,24,3,25,11,26,19,27,8,28,16,29,5,30,13,31,2,32,10,33,18,34,7,35,15,36,4,37,12,38), (1,22,16,25,10,20)(2,26,8,31,17,29)(3,30,19,37,5,38)(4,34,11,24,12,28)(6,23,14,36,7,27)(9,35)(13,32,15,21,18,33) |
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 $12$: $D_{6}$, $C_6\times C_2$ $18$: $S_3\times C_3$, $D_{9}$ $36$: $C_6\times S_3$, $D_{18}$ $54$: 18T19 $108$: 36T69 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 51 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $38988=2^{2} \cdot 3^{3} \cdot 19^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |