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);