Show commands:
Magma
magma: G := TransitiveGroup(21, 62);
Group action invariants
Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $62$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $D_7\wr S_3$ | ||
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: | (1,16,6,21,4,19,2,17,7,15,5,20,3,18)(8,10,12,14,9,11,13), (1,9,5,10)(2,11,4,8)(3,13)(6,12,7,14)(15,20,18,16,21,19,17) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $6$: $S_3$ $12$: $D_{6}$ $24$: $S_4$ $48$: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
28T414, 42T707, 42T708, 42T709, 42T710, 42T711, 42T712, 42T713, 42T714Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 65 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $16464=2^{4} \cdot 3 \cdot 7^{3}$ | 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: | 16464.br | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);