Show commands:
Magma
magma: G := TransitiveGroup(27, 1467);
Group action invariants
| Degree $n$: | $27$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $1467$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_3^7.C_3\wr C_3$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $3$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,14,22,3,13,24,2,15,23)(4,18,25,5,16,26,6,17,27)(7,10,19)(8,11,20)(9,12,21), (10,13,16)(11,14,17)(12,15,18), (7,8,9)(16,17,18)(25,26,27) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ x 13 $9$: $C_3^2$ x 13 $27$: $C_3^2:C_3$ x 12, 27T4 $81$: $C_3 \wr C_3 $ x 3, 27T18 x 4 $243$: 27T95, 27T100 x 2, 27T105 $729$: 27T220 x 3 $6561$: 27T691 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 9: $C_3 \wr C_3 $
Low degree siblings
27T1467 x 26Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 315 conjugacy class representatives for $C_3^7.C_3\wr C_3$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $177147=3^{11}$ | 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: | $7$ | ||
| Label: | 177147.bv | magma: IdentifyGroup(G);
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| Character table: | 315 x 315 character table |
magma: CharacterTable(G);