Show commands:
Magma
magma: G := TransitiveGroup(33, 31);
Group action invariants
Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $31$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{11}^3:A_4$ | ||
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: | (1,31,21,10,32,13,8,33,16,6,23,19,4,24,22,2,25,14,11,26,17,9,27,20,7,28,12,5,29,15,3,30,18), (1,26,16,6,23,18,11,31,20,5,28,22,10,25,13,4,33,15,9,30,17,3,27,19,8,24,21,2,32,12,7,29,14) | 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 11: None
Low degree siblings
44T142Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 149 conjugacy class representatives for $C_{11}^3:A_4$
magma: ConjugacyClasses(G);
Group invariants
Order: | $15972=2^{2} \cdot 3 \cdot 11^{3}$ | 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: | 15972.n | magma: IdentifyGroup(G);
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Character table: | 149 x 149 character table |
magma: CharacterTable(G);