Show commands:
Magma
magma: G := TransitiveGroup(44, 27);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $27$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}\times D_{22}$ | ||
| 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: | (1,29,3,43,6,35,8,28,10,42,11,33,13,26,16,40,17,31,20,23,22,37)(2,30,4,44,5,36,7,27,9,41,12,34,14,25,15,39,18,32,19,24,21,38), (1,30,13,25,3,44,16,39,6,36,17,32,8,27,20,24,10,41,22,38,11,34)(2,29,14,26,4,43,15,40,5,35,18,31,7,28,19,23,9,42,21,37,12,33) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$, 44T2 $242$: 22T7 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 11: None
Degree 22: 22T7
Low degree siblings
44T27 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 154 conjugacy class representatives for $C_{11}\times D_{22}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $484=2^{2} \cdot 11^{2}$ | 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: | 484.10 | magma: IdentifyGroup(G);
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| Character table: | 154 x 154 character table |
magma: CharacterTable(G);