Show commands:
Magma
magma: G := TransitiveGroup(28, 1854);
Group action invariants
Degree $n$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $1854$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $S_{28}$ | ||
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), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28) | 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 2: None
Degree 4: None
Degree 7: None
Degree 14: 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
There are 3,718 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $304888344611713860501504000000=2^{25} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23$ | 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: | 304888344611713860501504000000.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);