Show commands:
Magma
magma: G := TransitiveGroup(39, 48);
Group action invariants
| Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $48$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{13}\wr C_3$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $13$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,27,22,2,30,20,12,39,24,5,28,19,6,34,25,9,37,23,10,35,16,4,36,18,3,33,21,11,31,15,13,29,14,7,32,26,8,38,17), (1,36,19,2,33,25,12,31,23,5,29,16,6,32,18,9,38,21,10,27,15,4,30,14,3,39,26,11,28,17,13,34,22,7,37,20,8,35,24) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $13$: $C_{13}$ $39$: $C_{13}:C_3$ x 2, $C_{39}$ $507$: 39T20, 39T21 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T48 x 47Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 767 conjugacy class representatives for $C_{13}\wr C_3$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $6591=3 \cdot 13^{3}$ | 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: | 6591.13 | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);