Show commands:
Magma
magma: G := TransitiveGroup(33, 23);
Group action invariants
Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $23$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{11}\wr C_3$ | ||
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: | (1,18,31,2,22,25,3,15,30,4,19,24,5,12,29,6,16,23,7,20,28,8,13,33,9,17,27,10,21,32,11,14,26), (1,4,7,10,2,5,8,11,3,6,9)(12,20,17,14,22,19,16,13,21,18,15)(23,32,30,28,26,24,33,31,29,27,25) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $11$: $C_{11}$ $33$: $C_{33}$ $363$: 33T10 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T23 x 39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 473 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $3993=3 \cdot 11^{3}$ | 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: | 3993.6 | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);