Show commands:
Magma
magma: G := TransitiveGroup(21, 28);
Group action invariants
| Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7\wr C_3$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $7$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,20,8,3,16,14,5,19,13,7,15,12,2,18,11,4,21,10,6,17,9), (1,7,6,5,4,3,2)(8,10,12,14,9,11,13)(15,18,21,17,20,16,19) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $7$: $C_7$ $21$: $C_7:C_3$ x 2, $C_{21}$ $147$: 21T12, 21T13 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
21T28 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 133 conjugacy class representatives for $C_7\wr C_3$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1029=3 \cdot 7^{3}$ | 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: | 1029.15 | magma: IdentifyGroup(G);
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| Character table: | 133 x 133 character table |
magma: CharacterTable(G);