Show commands:
Magma
magma: G := TransitiveGroup(34, 12);
Group invariants
| Abstract group: | $C_{17}^2:C_4$ | magma: IdentifyGroup(G);
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| 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 | 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 $t$: | $12$ | 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: | $(1,31,15,22)(2,34,14,19)(3,20,13,33)(4,23,12,30)(5,26,11,27)(6,29,10,24)(7,32,9,21)(8,18)(16,25,17,28)$, $(1,22,14,27)(2,25,13,24)(3,28,12,21)(4,31,11,18)(5,34,10,32)(6,20,9,29)(7,23,8,26)(15,30,17,19)(16,33)$ | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $68$: $C_{17}:C_{4}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T12 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
76 x 76 character tablemagma: CharacterTable(G);
Regular extensions
Data not computed