Show commands:
Magma
magma: G := TransitiveGroup(39, 20);
Group action invariants
| Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{13}^2:C_3$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $13$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,23,38)(2,20,39)(3,17,29)(4,19,36)(5,16,33)(6,24,32)(7,22,35)(8,15,31)(9,26,30)(10,18,34)(11,21,27)(12,14,37)(13,25,28), (1,22,32)(2,15,30)(3,18,31)(4,26,35)(5,20,36)(6,14,29)(7,21,37)(8,25,33)(9,16,27)(10,24,28)(11,19,38)(12,23,34)(13,17,39) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $39$: $C_{13}:C_3$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T20 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 59 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: | 507.5 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);