Show commands:
Magma
magma: G := TransitiveGroup(14, 61);
Group action invariants
| Degree $n$: | $14$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $61$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $S_7\wr C_2$ | ||
| CHM label: | $[S(7)^{2}]2=S(7)wr2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (2,4,6,8,10,12,14), (10,12), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 7: None
Low degree siblings
28T1634, 28T1635, 28T1636, 42T3347Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 135 conjugacy class representatives for $S_7\wr C_2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $50803200=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2}$ | 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: | 50803200.a | magma: IdentifyGroup(G);
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| Character table: | 135 x 135 character table |
magma: CharacterTable(G);