Show commands:
Magma
magma: G := TransitiveGroup(21, 39);
Group action invariants
| Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_3^6:C_7$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $3$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,13,6,16,7,21,10)(2,14,4,17,8,20,11)(3,15,5,18,9,19,12), (1,15,4,16,8,19,12)(2,13,5,17,9,21,10)(3,14,6,18,7,20,11) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $7$: $C_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
21T39 x 51Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 111 conjugacy class representatives for $C_3^6:C_7$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $5103=3^{6} \cdot 7$ | 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: | 5103.4034 | magma: IdentifyGroup(G);
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| Character table: | 111 x 111 character table |
magma: CharacterTable(G);