Show commands:
Magma
magma: G := TransitiveGroup(44, 33);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{22}\wr C_2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $22$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,33,11,37,22,42,10,23,20,28,8,31,17,35,6,40,16,43,3,26,13,29)(2,34,12,38,21,41,9,24,19,27,7,32,18,36,5,39,15,44,4,25,14,30), (1,25,2,26)(3,39,4,40)(5,31,6,32)(7,23,8,24)(9,37,10,38)(11,30,12,29)(13,44,14,43)(15,35,16,36)(17,27,18,28)(19,42,20,41)(21,33,22,34) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$, 44T2 $88$: 44T5, 44T6 $242$: 22T7 $484$: 44T27 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: None
Degree 22: 22T7
Low degree siblings
44T33 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 275 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 968.26 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);