Show commands:
Magma
magma: G := TransitiveGroup(21, 30);
Group action invariants
| Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $30$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7^2:D_{21}$ | ||
| 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: | (1,15,5,19,2,16,6,20,3,17,7,21,4,18)(8,14)(9,13)(10,12), (1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,21)(16,20)(17,19) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $14$: $D_{7}$ $42$: $D_{21}$ $294$: 14T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
21T30 x 5, 42T267 x 6, 42T280 x 3, 42T283 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 77 conjugacy class representatives for $C_7^2:D_{21}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2058=2 \cdot 3 \cdot 7^{3}$ | 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: | 2058.q | magma: IdentifyGroup(G);
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| Character table: | 77 x 77 character table |
magma: CharacterTable(G);