Show commands:
Magma
magma: G := TransitiveGroup(22, 57);
Group action invariants
Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $57$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $S_{11}\wr C_2$ | ||
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: | (1,12,10,15,4,16,3,22,9,13,8,21)(2,19,6,14,7,18)(5,17,11,20), (1,19,11,22,9,18)(2,15,4,21,3,16,8,13,10,20,7,17,5,14,6,12) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T1966, 44T1967, 44T1968Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 1,652 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $3186701844480000=2^{17} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \cdot 11^{2}$ | 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: | no | magma: IsSolvable(G);
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Nilpotency class: | not nilpotent | ||
Label: | 3186701844480000.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);