Show commands:
Magma
magma: G := TransitiveGroup(22, 23);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $23$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}:C_{11}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,11,21,10,19,8,18,6,15,3,14)(2,12,22,9,20,7,17,5,16,4,13), (1,4,6,8,10,12,14,15,17,20,21)(2,3,5,7,9,11,13,16,18,19,22) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $11$: $C_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $C_{11}$
Low degree siblings
22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 104 conjugacy class representatives for $C_2^{10}:C_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $11264=2^{10} \cdot 11$ | 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: | 11264.f | magma: IdentifyGroup(G);
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| Character table: | 104 x 104 character table |
magma: CharacterTable(G);