Show commands:
Magma
magma: G := TransitiveGroup(28, 34);
Group action invariants
| Degree $n$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7\times D_{14}$ | ||
| 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: | (1,26,22,18,13,10,6,2,25,21,17,14,9,5)(3,8,12,16,20,23,28,4,7,11,15,19,24,27), (1,11,25,8,22,4,17,27,13,23,9,19,6,16)(2,12,26,7,21,3,18,28,14,24,10,20,5,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $7$: $C_7$ $14$: $D_{7}$, $C_{14}$ x 3 $28$: $D_{14}$, 28T2 $98$: $C_7 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T34 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 70 conjugacy class representatives for $C_7\times D_{14}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $196=2^{2} \cdot 7^{2}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 196.10 | magma: IdentifyGroup(G);
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| Character table: | 70 x 70 character table |
magma: CharacterTable(G);