Show commands:
Magma
magma: G := TransitiveGroup(22, 36);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $36$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.C_{11}:C_{10}$ | ||
| 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: | (1,15,5,10,4,2,16,6,9,3)(7,17,14,19,22,8,18,13,20,21)(11,12), (1,6,19,14,4)(2,5,20,13,3)(7,15,21,10,12,8,16,22,9,11) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $10$: $C_{10}$ $55$: $C_{11}:C_5$ $110$: 22T5 $56320$: 22T33 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $C_{11}:C_5$
Low degree siblings
22T36 x 2, 44T314 x 3, 44T315 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 80 conjugacy class representatives for $C_2^{10}.C_{11}:C_{10}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $112640=2^{11} \cdot 5 \cdot 11$ | 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: | 112640.b | magma: IdentifyGroup(G);
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| Character table: | 80 x 80 character table |
magma: CharacterTable(G);