Show commands:
Magma
magma: G := TransitiveGroup(33, 39);
Group action invariants
Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{11}^3:S_4$ | ||
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: | (1,19,25,3,22,24,5,14,23,7,17,33,9,20,32,11,12,31,2,15,30,4,18,29,6,21,28,8,13,27,10,16,26), (1,30,11,24)(2,25,10,29)(3,31,9,23)(4,26,8,28)(5,32,7,33)(6,27)(12,17,22,16,21,15,20,14,19,13,18) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $24$: $S_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
44T230Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 100 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $31944=2^{3} \cdot 3 \cdot 11^{3}$ | 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: | 31944.v | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);