Show commands:
Magma
magma: G := TransitiveGroup(21, 36);
Group action invariants
Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $36$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_7^3:A_4$ | ||
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: | (1,4)(2,3)(5,7)(8,11,14,10,13,9,12)(15,20)(16,19)(17,18), (1,13,17,3,9,16,5,12,15,7,8,21,2,11,20,4,14,19,6,10,18) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $12$: $A_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
28T275, 28T276 x 2, 42T390 x 2, 42T391, 42T406 x 2, 42T407Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 53 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $4116=2^{2} \cdot 3 \cdot 7^{3}$ | 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: | 4116.bv | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);