Show commands:
Magma
magma: G := TransitiveGroup(33, 33);
Group action invariants
Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_3^6.C_{22}$ | ||
Parity: | $-1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (1,4,7,12,15,17,20,22,27,30,33)(2,6,8,11,13,16,21,24,25,29,31,3,5,9,10,14,18,19,23,26,28,32), (1,33,28,26,22,21,16,13,11,9,5,2,31,29,27,23,19,17,14,12,7,6,3,32,30,25,24,20,18,15,10,8,4) | 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 $5346$: 33T24 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: $C_{11}$
Low degree siblings
33T33 x 21Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 66 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $16038=2 \cdot 3^{6} \cdot 11$ | 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: | 16038.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);