Show commands:
Magma
magma: G := TransitiveGroup(34, 29);
Group action invariants
| Degree $n$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $29$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^9:C_{17}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,5,9,13,18,21,25,29,33,3,7,11,15,19,23,28,32)(2,6,10,14,17,22,26,30,34,4,8,12,16,20,24,27,31), (1,32,28,23,19,15,11,8,4,33,29,25,22,17,14,9,5,2,31,27,24,20,16,12,7,3,34,30,26,21,18,13,10,6) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $17$: $C_{17}$ $34$: $C_{34}$ $4352$: 34T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 17: $C_{17}$
Low degree siblings
34T29 x 14Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 64 conjugacy class representatives for $C_2^9:C_{17}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $8704=2^{9} \cdot 17$ | 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: | 8704.b | magma: IdentifyGroup(G);
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| Character table: | 64 x 64 character table |
magma: CharacterTable(G);