Show commands:
Magma
magma: G := TransitiveGroup(34, 11);
Group action invariants
| Degree $n$: | $34$ | 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: | $D_{17}^2$ | ||
| 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: | (1,4)(2,3)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(18,23)(19,22)(20,21)(24,34)(25,33)(26,32)(27,31)(28,30), (1,32,6,21,11,27,16,33,4,22,9,28,14,34,2,23,7,29,12,18,17,24,5,30,10,19,15,25,3,31,8,20,13,26) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $34$: $D_{17}$ x 2 $68$: $D_{34}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T11 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 100 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1156=2^{2} \cdot 17^{2}$ | 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: | 1156.13 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);