Show commands:
Magma
magma: G := TransitiveGroup(22, 44);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{11}.M_{11}$ | ||
| 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: | (1,21,10,18,11,15,5,4,2,22,9,17,12,16,6,3)(7,8)(13,19)(14,20), (1,15,7,13,11,10,17,4,2,16,8,14,12,9,18,3)(5,19)(6,20) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $7920$: $M_{11}$ $15840$: 22T26 $8110080$: 22T43 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $M_{11}$
Low degree siblings
22T44, 44T613, 44T615 x 2, 44T617 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 104 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $16220160=2^{15} \cdot 3^{2} \cdot 5 \cdot 11$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 16220160.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);