Show commands:
Magma
magma: G := TransitiveGroup(34, 10);
Group invariants
| Abstract group: | $C_{17}\times D_{17}$ | magma: IdentifyGroup(G);
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| Order: | $578=2 \cdot 17^{2}$ | 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 | 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 $t$: | $10$ | 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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| $\card{\Aut(F/K)}$: | $17$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | $(1,8,15,5,12,2,9,16,6,13,3,10,17,7,14,4,11)(18,28,21,31,24,34,27,20,30,23,33,26,19,29,22,32,25)$, $(1,25,14,23,10,21,6,19,2,34,15,32,11,30,7,28,3,26,16,24,12,22,8,20,4,18,17,33,13,31,9,29,5,27)$ | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $17$: $C_{17}$ $34$: $D_{17}$, $C_{34}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T10 x 7Siblings 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
Character table not computed
magma: CharacterTable(G);
Regular extensions
Data not computed