Show commands:
Magma
magma: G := TransitiveGroup(33, 28);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_{11}^2:D_{33}$ | ||
| 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: | (1,17,6,19,11,21,5,12,10,14,4,16,9,18,3,20,8,22,2,13,7,15)(23,24)(25,33)(26,32)(27,31)(28,30), (1,28,21,8,30,16,4,32,22,11,23,17,7,25,12,3,27,18,10,29,13,6,31,19,2,33,14,9,24,20,5,26,15) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $22$: $D_{11}$ $66$: $D_{33}$ $726$: 33T13 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T28 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 253 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $7986=2 \cdot 3 \cdot 11^{3}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 7986.j | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);