Show commands:
Magma
magma: G := TransitiveGroup(39, 49);
Group action invariants
| Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $49$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_3^6:C_{13}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $3$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,36,30,22,16,12,4,38,32,26,19,15,8)(2,34,28,23,17,10,5,39,33,27,20,13,9)(3,35,29,24,18,11,6,37,31,25,21,14,7), (1,29,18,6,31,21,7,36,24,10,39,27,14)(2,30,16,4,32,19,8,34,22,11,37,25,15)(3,28,17,5,33,20,9,35,23,12,38,26,13) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $13$: $C_{13}$ $351$: 27T134 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 13: $C_{13}$
Low degree siblings
39T49 x 25Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 69 conjugacy class representatives for $C_3^6:C_{13}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $9477=3^{6} \cdot 13$ | 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: | 9477.4041 | magma: IdentifyGroup(G);
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| Character table: | 69 x 69 character table |
magma: CharacterTable(G);