Show commands:
Magma
magma: G := TransitiveGroup(42, 4749);
Group action invariants
| Degree $n$: | $42$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $4749$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_3^{13}.C_2.\PSL(2,7)$ | ||
| 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: | (1,4,38,7,3,6,39,8,2,5,37,9)(10,42,33,19,12,41,31,21,11,40,32,20)(13,35,14,36,15,34)(16,28,23,27,17,29,24,25,18,30,22,26), (1,30,20,22,8,41,3,29,21,24,9,42,2,28,19,23,7,40)(4,15,12,25,35,31,5,14,11,26,34,32,6,13,10,27,36,33)(16,39)(17,38)(18,37) | magma: Generators(G);
|
Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $168$: $\GL(3,2)$ $336$: 14T17 $122472$: 21T104 $244944$: 42T1496 $734832$: 21T119 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 7: $\GL(3,2)$
Degree 14: 14T17
Degree 21: None
Low degree siblings
42T4749Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $535692528=2^{4} \cdot 3^{14} \cdot 7$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 535692528.l | magma: IdentifyGroup(G);
| |
| Character table: | not computed |
magma: CharacterTable(G);