Show commands:
Magma
magma: G := TransitiveGroup(38, 21);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_{19}^2:(C_3\times S_3)$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,13,6,18,11,4,16,9,2,14,7,19,12,5,17,10,3,15,8)(20,36,34)(21,24,26)(22,31,37)(23,38,29)(25,33,32)(27,28,35), (1,20,19,22,12,36)(2,37,7,27,4,33)(3,35,14,32,15,30)(5,31,9,23,18,24)(6,29,16,28,10,21)(8,25,11,38,13,34)(17,26) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $S_3$, $C_6$ $18$: $S_3\times C_3$ 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 54 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $6498=2 \cdot 3^{2} \cdot 19^{2}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 6498.n | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);