Show commands:
Magma
magma: G := TransitiveGroup(13, 8);
Group action invariants
Degree $n$: | $13$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $8$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $A_{13}$ | ||
CHM label: | $A13$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (3,4,5,6,7,8,9,10,11,12,13), (1,2,3) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Prime degree - 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
The 55 conjugacy class representatives for $A_{13}$
magma: ConjugacyClasses(G);
Group invariants
Order: | $3113510400=2^{9} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$ | 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: | no | magma: IsSolvable(G);
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Nilpotency class: | not nilpotent | ||
Label: | 3113510400.a | magma: IdentifyGroup(G);
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Character table: | 55 x 55 character table |
magma: CharacterTable(G);