Show commands:
Magma
magma: G := TransitiveGroup(27, 434);
Group action invariants
Degree $n$: | $27$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $434$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_9\wr C_3$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $9$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (10,18,14,11,16,15,12,17,13), (1,14,24)(2,15,23)(3,13,22)(4,17,25)(5,18,27)(6,16,26)(7,10,20)(8,11,19)(9,12,21) | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $3$: $C_3$ x 4 $9$: $C_9$ x 3, $C_3^2$ $27$: $C_9:C_3$ x 2, $C_3^2:C_3$, 27T2 $81$: $C_3 \wr C_3 $, 27T17, 27T20, 27T23 $243$: 27T104, 27T108 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 9: $C_3 \wr C_3 $
Low degree siblings
27T434 x 26Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computed
magma: ConjugacyClasses(G);
Group invariants
Order: | $2187=3^{7}$ | 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: | $5$ | ||
Label: | 2187.366 | magma: IdentifyGroup(G);
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Character table: | not computed |
magma: CharacterTable(G);