Show commands:
Magma
magma: G := TransitiveGroup(26, 11);
Group action invariants
| Degree $n$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $11$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{13}\times D_{13}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $13$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,23,13,18,12,26,11,21,10,16,9,24,8,19,7,14,6,22,5,17,4,25,3,20,2,15), (1,15,8,24,2,20,9,16,3,25,10,21,4,17,11,26,5,22,12,18,6,14,13,23,7,19) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $13$: $C_{13}$ $26$: $D_{13}$, $C_{26}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 13: None
Low degree siblings
26T11 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 104 conjugacy class representatives for $C_{13}\times D_{13}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $338=2 \cdot 13^{2}$ | 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: | 338.3 | magma: IdentifyGroup(G);
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| Character table: | 104 x 104 character table |
magma: CharacterTable(G);