Group action invariants
| Degree $n$: | $38$ | |
| Transitive number $t$: | $45$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,33,10,21,13,36,14,22,8,30,6,20,18,23,3,24,17,37,9,35,19,28,16,32,15,27,2,38,4,29,11,26,7,25,12,31)(5,34), (1,29,6,34,16,25,17,26,19,28,4,32,12,21,9,37,3,31,10,38,5,33,14,23,13,22,11,20,7,35,18,27,2,30,8,36)(15,24) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $4$: $C_4$ $6$: $S_3$, $C_6$ $9$: $C_9$ $12$: $C_{12}$, $C_3 : C_4$ $18$: $S_3\times C_3$, $D_{9}$, $C_{18}$ $36$: $C_3\times (C_3 : C_4)$, $C_{36}$, 36T9 $54$: $C_9\times S_3$, 18T19 $108$: 36T62, 36T68 $162$: 18T74 $324$: 36T462 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 118 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: | not available |
| Character table: not available. |