Show commands:
Magma
magma: G := TransitiveGroup(33, 27);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $27$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}\wr S_3$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $11$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,21,11,17,10,13,9,20,8,16,7,12,6,19,5,15,4,22,3,18,2,14)(23,30,26,33,29,25,32,28,24,31,27), (1,4,7,10,2,5,8,11,3,6,9)(12,30,17,28,22,26,16,24,21,33,15,31,20,29,14,27,19,25,13,23,18,32) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $11$: $C_{11}$ $22$: 22T1 $66$: 33T2 $726$: 33T13 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T27 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 418 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $7986=2 \cdot 3 \cdot 11^{3}$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 7986.i | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);