Show commands:
Magma
magma: G := TransitiveGroup(21, 34);
Group action invariants
| Degree $n$: | $21$ | 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: | $C_7^3:C_3^2$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,11,20,2,9,16,3,14,19,4,12,15,5,10,18,6,8,21,7,13,17), (1,3,4)(2,7,6)(8,9,13)(11,14,12)(16,19,17)(18,20,21) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ x 4 $9$: $C_3^2$ $21$: $C_7:C_3$ x 3 $63$: 21T7 x 3 $441$: 21T21 x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
21T34 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 63 conjugacy class representatives for $C_7^3:C_3^2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $3087=3^{2} \cdot 7^{3}$ | 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: | 3087.j | magma: IdentifyGroup(G);
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| Character table: | 63 x 63 character table |
magma: CharacterTable(G);