Show commands:
Magma
magma: G := TransitiveGroup(33, 32);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $32$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}^3:D_6$ | ||
| 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: | (1,31,9,27,6,23,3,30,11,26,8,33,5,29,2,25,10,32,7,28,4,24)(12,15,18,21,13,16,19,22,14,17,20), (1,2)(3,11)(4,10)(5,9)(6,8)(12,24,17,26,22,28,16,30,21,32,15,23,20,25,14,27,19,29,13,31,18,33) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $6$: $S_3$ $12$: $D_{6}$ $22$: $D_{11}$ $44$: $D_{22}$ $132$: 33T5 $1452$: 33T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T32 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 221 conjugacy class representatives for $C_{11}^3:D_6$
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.f | magma: IdentifyGroup(G);
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| Character table: | 221 x 221 character table |
magma: CharacterTable(G);