Show commands:
Magma
magma: G := TransitiveGroup(34, 15);
Group invariants
| Abstract group: | $D_{17}\wr C_2$ | magma: IdentifyGroup(G);
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| Order: | $2312=2^{3} \cdot 17^{2}$ | 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 | magma: NilpotencyClass(G);
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Group action invariants
| Degree $n$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $15$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | $(1,24,3,18,5,29,7,23,9,34,11,28,13,22,15,33,17,27,2,21,4,32,6,26,8,20,10,31,12,25,14,19,16,30)$, $(1,26,16,20)(2,29,15,34)(3,32,14,31)(4,18,13,28)(5,21,12,25)(6,24,11,22)(7,27,10,19)(8,30,9,33)(17,23)$ | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T13, 34T15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computedmagma: ConjugacyClasses(G);
Character table
65 x 65 character tablemagma: CharacterTable(G);
Regular extensions
Data not computed