Show commands:
Magma
magma: G := TransitiveGroup(21, 130);
Group action invariants
| Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $130$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_3^6.S_7$ | ||
| 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: | (1,16,4,12,7,21,13)(2,17,5,10,8,20,14)(3,18,6,11,9,19,15), (1,15,19,4,12,8,2,13,21,5,10,9,3,14,20,6,11,7)(16,18,17) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5040$: $S_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
42T2268Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 143 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $3674160=2^{4} \cdot 3^{8} \cdot 5 \cdot 7$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 3674160.c | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);