Show commands:
Magma
magma: G := TransitiveGroup(39, 50);
Group action invariants
| Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $50$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_3^6:C_{13}$ | ||
| Parity: | $1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $3$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,31,24,15,4,35,27,18,8,38,30,19,10)(2,32,22,13,5,36,25,16,9,39,28,20,11)(3,33,23,14,6,34,26,17,7,37,29,21,12), (1,37,36,33,29,25,23,20,17,15,12,8,5)(2,38,34,31,30,26,24,21,18,13,10,9,6)(3,39,35,32,28,27,22,19,16,14,11,7,4) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $13$: $C_{13}$ $351$: 27T134 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 13: $C_{13}$
Low degree siblings
39T50 x 25Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 69 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $9477=3^{6} \cdot 13$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 9477.4043 | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);