Show commands:
Magma
magma: G := TransitiveGroup(28, 47);
Group action invariants
| Degree $n$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $47$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{14}\wr C_2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $14$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,25,5,16,9,20,13,23,3,28,8,18,12,21,2,26,6,15,10,19,14,24,4,27,7,17,11,22), (1,21)(2,22)(3,24)(4,23)(5,26)(6,25)(7,28)(8,27)(9,15)(10,16)(11,18)(12,17)(13,19)(14,20) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $7$: $C_7$ $8$: $D_{4}$ $14$: $D_{7}$, $C_{14}$ x 3 $28$: $D_{14}$, 28T2 $56$: 28T5, 28T6 $98$: $C_7 \wr C_2$ $196$: 28T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T47 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 119 conjugacy class representatives for $C_{14}\wr C_2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $392=2^{3} \cdot 7^{2}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 392.27 | magma: IdentifyGroup(G);
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| Character table: | 119 x 119 character table |
magma: CharacterTable(G);