Show commands:
Magma
magma: G := TransitiveGroup(16, 1945);
Group action invariants
| Degree $n$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $1945$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^7.S_8$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,16,2,15)(3,8,9,13,6)(4,7,10,14,5)(11,12), (1,10,8,15,13)(2,9,7,16,14)(3,11,5)(4,12,6) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $40320$: $S_8$ $2580480$: 56T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 8: $S_8$
Low degree siblings
16T1945, 32T2711885Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 100 conjugacy class representatives for $C_2^7.S_8$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $5160960=2^{14} \cdot 3^{2} \cdot 5 \cdot 7$ | 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: | 5160960.b | magma: IdentifyGroup(G);
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| Character table: | 100 x 100 character table |
magma: CharacterTable(G);