Show commands:
Magma
magma: G := TransitiveGroup(15, 104);
Group action invariants
| Degree $n$: | $15$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $104$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $S_{15}$ | ||
| CHM label: | $S15$ | ||
| 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: | (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 5: None
Low degree siblings
30T5467Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 176 conjugacy class representatives for $S_{15}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1307674368000=2^{11} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$ | 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: | 1307674368000.a | magma: IdentifyGroup(G);
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| Character table: | 176 x 176 character table |
magma: CharacterTable(G);