Show commands:
Magma
magma: G := TransitiveGroup(39, 21);
Group action invariants
Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{13}:C_{39}$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $13$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (1,28,22,11,35,20,9,31,24,2,38,19,13,39,25,10,37,23,12,33,16,7,32,18,4,30,21,5,34,15,8,36,14,3,29,26,6,27,17), (1,21,27,8,23,34,7,24,33,13,17,38,11,15,28,3,16,36,4,19,32,10,22,39,9,14,35,6,18,29,5,25,30,12,20,37,2,26,31) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $13$: $C_{13}$ $39$: $C_{13}:C_3$, $C_{39}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T21 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 91 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $507=3 \cdot 13^{2}$ | 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: | 507.3 | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);