Show commands:
Magma
magma: G := TransitiveGroup(22, 29);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $29$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.D_{11}$ | ||
| 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: | (1,13,4,16,6,17,8,19,9,22,11)(2,14,3,15,5,18,7,20,10,21,12), (1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16,8,15)(9,13)(10,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $22$: $D_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $D_{11}$
Low degree siblings
22T29 x 30, 22T30 x 31, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 100 conjugacy class representatives for $C_2^{10}.D_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $22528=2^{11} \cdot 11$ | 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: | 22528.d | magma: IdentifyGroup(G);
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| Character table: | 100 x 100 character table |
magma: CharacterTable(G);