Show commands:
Magma
magma: G := TransitiveGroup(33, 46);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{11}\wr S_3$ | ||
| 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: | (1,11,10,9,8,7,6,5,4,3,2)(12,31,22,24)(13,27,21,28)(14,23,20,32)(15,30,19,25)(16,26,18,29)(17,33), (1,23,6,31)(2,29,5,25)(3,24,4,30)(7,26,11,28)(8,32,10,33)(9,27)(12,20)(13,19)(14,18)(15,17)(21,22) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $6$: $S_3$ $12$: $D_{6}$ $24$: $S_4$ $48$: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
44T293Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 140 conjugacy class representatives for $D_{11}\wr S_3$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $63888=2^{4} \cdot 3 \cdot 11^{3}$ | 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: | 63888.q | magma: IdentifyGroup(G);
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| Character table: | 140 x 140 character table |
magma: CharacterTable(G);