Show commands:
Magma
magma: G := TransitiveGroup(26, 13);
Group action invariants
| Degree $n$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $13$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{13}^2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,17,9,21,4,25,12,16,7,20,2,24,10,15,5,19,13,23,8,14,3,18,11,22,6,26), (1,24,3,23,5,22,7,21,9,20,11,19,13,18,2,17,4,16,6,15,8,14,10,26,12,25) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $26$: $D_{13}$ x 2 $52$: $D_{26}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 13: None
Low degree siblings
26T13 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 64 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $676=2^{2} \cdot 13^{2}$ | 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: | 676.13 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);