Show commands:
Magma
magma: G := TransitiveGroup(1, 1);
Group action invariants
Degree $n$: | $1$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $1$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | Trivial | ||
CHM label: | $Trivial group$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | yes | magma: IsPrimitive(G);
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Nilpotency class: | $0$ | magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | None needed | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 1 - None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Cycle Type | Size | Order | Representative |
$1$ | $1$ | $1$ | $()$ |
magma: ConjugacyClasses(G);
Group invariants
Order: | $1$ | magma: Order(G);
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Cyclic: | yes | magma: IsCyclic(G);
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Abelian: | yes | magma: IsAbelian(G);
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Solvable: | yes | magma: IsSolvable(G);
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Label: | 1.1 | magma: IdentifyGroup(G);
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Character table: |
1a X.1 1 |
magma: CharacterTable(G);